Book-Tax Differences, Uncertainty about Information Quality, and Cost of Capital

Dan S. Dhaliwal University of Arizona

Hye Seung “Grace” Lee University of Arizona

Morton Pincus

University of California, Irvine

October 11, 2009

Earlier versions of this working paper were presented at Chinese University of Hong Kong, University of British Columbia, University of California, Berkeley, the 2008 American Accounting Association’s Atlantic Regional meeting, the 2008 AAA annual meeting, and the 2008 California State University-Fullerton’s Conference on Corporate Reporting and Governance. We gratefully acknowledge the helpful comments we received from participants at these forums, especially Tom Omer who discussed the paper at the AAA annual meeting and Richard Sloan. This study previously circulated under the title “Variability of Book-Tax Differences, Information Uncertainty, and Implied Cost of Capital” and “Book-Tax Differences, Uncertainty about Fundamentals and Information Quality, and Cost of Capital.”

Book-Tax Differences, Uncertainty about Information Quality, and Cost of Capital

ABSTRACT. We investigate whether differences in implied cost of equity capital across firms are

associated with (1) differences between book and taxable incomes (BTDs) and (2) an earnings quality

measure derived from BTDs. Prior research suggests BTDs reflect firms’ earnings management and

tax planning activities and their economic fundamentals (including credit risk). We conjecture a link

to cost of capital if BTDs capture information uncertainty regarding managerial discretion over

accounting choices. Our initial analysis indicates that several BTD variables, especially the standard

deviation of BTDs over time, are positively related to cost of capital. We then estimate a model to

predict BTDs and focus on the residual, the portion not predicted by fundamentals and tax

aggressiveness, which should capture information uncertainty due to managerial discretion over

financial reporting. The standard deviation of the residuals over time is our BTD-based earnings

quality measure, and it is positively related to cost of capital. The results are robust to sensitivity

analyses, including the use of deferred tax expense, controlling for alternative earnings quality

measures, and estimating cost of capital at the portfolio level. Given the framework of Lambert et

al.’s (2007) CAPM-based model, our research examines whether our BTD-derived earnings quality

measure reflects information effects related to cost of capital, consistent with empirical estimates of

beta using historical returns not fully capturing information effects. If multiple risk factors are

allowed (e.g., Indjejikian 2007), then our research can be viewed as an attempt to separately identify

firm innate characteristics and discretionary information effects and contributes to research seeking to

determine whether there is an “information risk factor” (e.g., Francis et al. 2004, 2005; Yee 2006).

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I. INTRODUCTION

The purpose of this study is twofold: (1) we investigate a link between book-tax differences

(BTDs) and implied cost of equity capital; and (2) examine an earnings quality measure we derive

from BTDs and its relation to cost of capital. BTDs are a potentially fruitful source for a firm’s

information environment (i.e., information captured by both book income and taxable income) for

several reasons, including that prior research indicates (i) that both book and taxable incomes are

incrementally informative about firm value beyond the other, and (ii) that BTDs have the potential of

capturing firm fundamentals and managerial discretion over tax planning and financial reporting. We

conjecture a link to cost of capital to the extent BTDs reflect information uncertainty with regard to

managerial discretion over accounting choices. The earnings quality variable we derive is the portion

of BTDs not predicted by firm fundamentals (operating, investing, and financing activities, growth,

and firm size) or tax aggressiveness, and reflects information from two contemporaneous measures of

performance, in contrast to earnings quality measures based solely on book income.

Our research can be viewed within the framework provided by the single-factor CAPM-based

model developed by Lambert et al. (2007) or as an attempt to separately identify firm innate

characteristics and discretionary information effects (Yee 2006; Francis et al. 2008). That is, our

research examines whether BTDs and the earnings quality measure we derive from BTDs reflect

information effects that are related to cost of capital, which would be consistent with empirical

estimates of beta based on historical returns not fully capturing information effects, consistent with

Lambert et al.’s (2007) model. On the other hand, if one allows for the possibility of multiple risk

factors (e.g., Indjejikian 2007), then our exploration of a relation between cost of capital and both

BTDs and our BTD-based earnings quality measure can be motivated in the same manner as prior

research that seeks to determine whether there is an “information risk factor” (e.g., Francis et al. 2005).

As is well known, U.S. shareholder reporting and tax reporting differ in their primary

purposes: external reporting to shareholders and other parties seeks to provide information useful in

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making informed judgments and rational decisions about firm value and managerial stewardship; tax

reporting reflects the needs of the taxing authority to raise revenue and provides incentives favoring

certain economic and other activities. Hence, even though book income and taxable income are each

measures of performance, they can reflect different information.

Further, income measures generally are computed based on accrual accounting, but taxable

income reflects more elements of cash basis accounting than book income (Hanlon 2005; Graham et al.

2008). Computing book income primarily based on accrual accounting versus measuring taxable

income using a hybrid accrual basis/cash basis approach offers a possible explanation for why taxable

income and book income are incrementally useful beyond the other in explaining firm value (Hanlon et

al. 2005). Another, somewhat related possibility is that taxable income generally is computed

following a more rules-based (i.e., “bright lines”) approach than is book income. While U.S.

generally accepted accounting principles include standards that are rules (and guidance) oriented, and

even though opportunities exist in tax reporting to structure transactions to avoid (or evade) income

taxes, researchers generally recognize there is more discretion permitted in financial reporting than in

tax reporting (e.g., Phillips et al 2003; Hanlon 2005), for example, the greater ability to provide for

losses. Further, BTDs reflect tensions that are often present between book and tax reporting

(Badertscher et al. 2009a, 2009b; Hunt et al. 1996). In sum, book income and taxable income are two

components of a firm’s overall information environment and reveal firm characteristics that neither

income measure fully captures by itself. Therefore, we conjecture that information in BTDs reflects

the quality of the total information provided by both income measures and assists investors in

assessing firm risk and potentially reflects information risk. We note that others have also drawn a

link between BTDs and earnings quality (e.g., Lev and Nissim 2004; Yee 2006; Ayres et al. 2009).

For example, Revsine et al. (1999, 633) argue that “A widening excess of book income over taxable

income ... represent[s] a potential danger signal that ... might be an indication of deteriorating earnings

quality.”

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We initially investigate this by exploring the relation between various measures of BTDs and

firms’ cost of equity capital. We then derive a proxy for earnings quality that is the portion of BTDs

not predicted by firm fundamentals and tax aggressiveness and examine whether this earnings quality

measure is related to cost of capital. Demonstrating such a link supports an economic role for

accounting information in resource allocations in capital markets (Francis et al. 2008a; Graham et al.

2008). Our analysis is motivated by the fact that there is no definitive theory of earnings quality (e.g.,

Schipper and Vincent 2003) and at the same time, precision of earnings is an overarching indicator of

financial reporting quality (e.g., Francis et al. 2008a).

We analyze a sample of firm-years from 1982 through 2006 and begin by investigating

whether various measures of total BTDs – the presence of large positive and large negative current

year BTDs, absolute value of BTDs, and standard deviation of BTDs over time – are related to cost of

equity capital. We estimate cost of capital in multiple ways, including using the average of four

alternative firm-specific ex ante measures and sensitivity tests based on the separate measures,

simultaneously estimating cost of capital and growth rate at the portfolio level, and realized stock

returns. After controlling for other factors that explain cost of capital, we find that the BTD variables

generally are positively related to cost of capital, with the standard deviation of total BTDs over time

being related to cost of capital most consistently relative to other BTD measures.

Next, we model total BTDs as a function of firms’ fundamentals (operating, investing, and

financing activities, growth, and size) and tax aggressiveness, and focus on the residual from the

estimated model (i.e., the portion not predicted by fundamentals and tax aggressiveness). The

residuals should capture managerial discretion over the financial reporting process and thus proxy for

information uncertainty about earnings, which is the basis for our earnings quality variable. We find

that the standard deviation of the unpredicted portion of BTDs over time is positively related to cost of

capital. Additional analyses indicate that our earnings quality measure is positively related to other

indicators of accounting quality derived from book income (Francis et al. 2008a), and that our results

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hold after controlling for these other earnings quality measures. Our inferences are generally

unchanged after considering a battery of sensitivity analyses and when using temporary BTDs in place

of total book-tax difference variables. Overall, the results are consistent with our BTD-derived

measure of earnings quality capturing information effects not fully reflected in return beta (possibly

due to estimation error) and other determinants of cost of capital and also consistent with it being an

information risk factor.

We organize the remainder of the paper as follows. Section II provides an overview of prior

literature and our hypothesis development. Section III outlines the empirical analysis and sample

selection procedures. We report the results of our main empirical analysis and sensitivity tests in

Section IV, and conclude in Section V.

II. PRIOR RESEARCH AND HYPOTHESIS DEVELOPMENT

A growing body of research investigates the general question of whether book-tax differences

are informative about aspects of firms’ earnings and other fundamental characteristics and their tax

planning and earnings management activities. This line of research is important because it provides

evidence on the usefulness of taxable income as a supplementary measure to financial reporting (i.e.,

book) income in assessing firm value and on the usefulness of book-tax differences as an indicator of

earnings management and/or tax aggressiveness.1 We contribute to this line of research by examining

the extent to which BTDs capture firms’ information uncertainty and are related to cost of equity

capital, thereby shedding light on whether the information captured by the differences between book

and taxable incomes yield an indicator of information quality.

1 The research is also relevant to the current policy debate about book-tax conformity, although a thorough examination of that issue is beyond the scope of this study. Book-tax conformity would eliminate BTDs thereby reducing the ability of financial report users to consider BTDs in drawing inferences about firm value and earnings and tax management activities. However, book-tax conformity likely would make tax shelter and earnings management activities more costly since managers would be more constrained in maximizing book income and minimizing taxable income.

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Prior Research

There is considerable evidence of earnings management and tax planning activities being

reflected in financial statement variables. Studies demonstrate firms’ tax minimization behavior

either by assuming that book income conforms to taxable income, as in Scholes et al. (1990) who find

managers shifted income to the following year when tax rates would be lower, or by exploiting the

LIFO book-tax conformity rule, as in Dhaliwal et al. (1994) who show firms liquidated LIFO

inventory layers to increase book income.2

Focusing on BTDs, Joos et al. (2000) interpret evidence of a weaker earnings-security return

relation in the presence of large temporary BTDs (i.e., large deferred tax expense, DTE) as suggesting

that firms managed earnings opportunistically and investors recognized these actions and placed a

lower weight on earnings in valuation. Phillips et al. (2003) find that DTE is incrementally useful

beyond accruals variables in detecting certain types of earnings management. Badertscher et al

(2009a) show that BTDs are useful in predicting firms that restate earnings downward due to

accounting irregularities, and that such restatement firms appear to trade off tax benefits against the

costs of being detected as an earnings manager when deciding to engage in upward earnings

management strategies.

Book and taxable incomes are calculated in ways that often differ due to differences in the

respective primary purposes: providing information useful for decision-making, versus raising funds

for the taxing authority and providing incentives to promote certain activities. Thus, there likely will

be a gap between the two contemporaneous performance measures that reflects differences in income

measurement related to certain firm activities (e.g., bad debts, depreciation), irrespective of any

2 There is a large body of research on the choice and impact of LIFO. See, e.g., Sunder (1973), Biddle (1980), Ricks (1982), Dopuch and Pincus (1988), Hand (1994), Hunt et al. (1996), and Pincus (1997).

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earnings or tax management strategies firms employ.3

Furthermore, Hanlon et al. (2005) and Ayres et al. (2008) demonstrate that taxable income and

book income are incrementally informative beyond the other in assessing firm value, with book

income being relatively more informative.4 Hanlon (2005) finds that large positive and negative

temporary BTDs are informative about earnings persistence, and Lev and Nissim (2004) show the ratio

the taxable income-to-book income predicts earnings growth. The literature also suggests that BTDs

reflect firms’ economic characteristics. Hanlon and Krishnan (2006) argue that larger BTDs can be

indicative of more complex firms, such as multinationals, and Jones and Noga (2006) show that higher

BTDs are associated with higher probabilities of financial distress. Moreover, Ayres et al. (2009) and

Crabtree and Maher (2009) find that firms with large positive or negative levels of, or changes in,

BTDs have lower credit ratings and thus higher credit risk. Such findings suggest BTDs map into

aspects of firms’ underlying fundamentals and reveal cross-sectional differences that neither income

measure fully reflects by itself.

Overall, previous research is consistent with cross-sectional variation in BTDs arising from

differences in book and tax reporting that reflect features of firms’ underlying fundamentals not fully

reflected in either of the earnings measures, as well as earnings management and tax aggressiveness

activities. A possible interpretation of these results is that book and tax incomes, being two measures

of current performance, are together informative beyond the accrual and operating cash flow

components of book income alone. This could be so because the computation of taxable income

places relatively more emphasis on rules and has more of a cash-basis orientation than book income,

and these differences likely are accentuated by the differing objectives of book and tax reporting.

3 Desai (2003) evaluates factors frequently recognized as explaining BTDs (depreciation, foreign source income, stock options) and finds they account for less than half of the growth in BTDs over a 20-year period. 4 Taxable income likely has greater measurement error since it is not disclosed but must be estimated. Also, being closer to cash basis, taxable income does not reflect most write-downs or provisions.

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Book-Tax Difference Variables

Total BTDs reflect temporary and permanent differences per SFAS No. 109. As outlined

above, most prior BTD-related research uses either deferred tax expense (DTE), the measure of

temporary differences, or total BTDs. We focus on total BTDs (or variations thereof) in our primary

analysis, but also consider DTE as well.

We note that results of prior BTD research are generally based on single year levels (or

changes) of book and taxable incomes. However, the information reflected in single years’ BTDs

may be limited relative to the information reflected in multiple years’ observations. Weber (2009),

building on Lev and Nissim (2004), finds that analysts’ earnings forecasts generally do not fully reflect

the information in BTDs, which helps explain an association between current BTDs and future stock

returns. Weber’s (2009) results are consistent with the capital market not fully impounding the

information in the ratio of tax-to-book incomes in the period these income measures are reported.5

The absence of an immediate market response that fully impounds current BTDs suggests the

possibility that information reflected in a BTD variable that spans the current and prior years may be

more reliably captured in current period capital market variables.

Moreover, variability in BTDs over time may capture uncertainty about the quality of firms’

information. Variability measures are widely recognized as indicators of risk and uncertainty, and the

inverse of variability measures reflects precision of information, which a number of researchers

associate with earnings quality (e.g., Verrecchia 1980; Dechow and Schrand 2004; Francis et al. 2008a).

The idea we are suggesting is that variability in BTDs over time captures a time-series of managerial

decisions that can be altered in different periods. Thus, the standard deviation of BTDs over time

may reflect uncertainty about firms’ discretionary actions over financial reporting and tax planning and

about the quality of firms’ information, and perhaps do so better than other BTD variables. This idea

5 Graham et al. (2008) note that since tax return data are not publicly available, the information that market participants have about firms’ tax reporting is generally based on the accounting for income taxes in firms’ external shareholder reports.

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is similar in spirit to Dechow and Dichev’s (2002) use of variability over multiple years to derive their

accrual quality measure (e.g., Francis et al. 2005).

Innate and Discretionary Components of BTDs

We develop a model of BTDs with independent variables that capture innate firm factors:

operating, investing and financing activities, growth, firm size, and tax aggressiveness. All else equal

(stable accounting standards or tax rules, and controlling for tax aggressiveness and firm fundamentals),

variability in management’s financial reporting decisions over time is a likely source of information

uncertainty and the basis for an information uncertainty measure. Hence, the model’s residual, or

unpredicted component, is our proxy for information uncertainty and thus for our BTD-based earnings

quality measure. This decomposition of BTDs is consistent with the approach taken by Francis et al.

(2005) and modeled by Yee (2006) and suggested with regard to taxes by Graham et al. (2009).

Overall, we believe that our proposed measure of earnings quality, as well as our research

approach, is consistent with Francis et al.’s (2008a, 262) view of earnings quality as a “multi-

dimensional construct.” They argue as follows:

“First, we associate earnings quality with precision, in the sense that higher quality earnings are more precise with respect to an underlying valuation-relevant construct that earnings is intended to describe….Second, we take a capital allocation view of earnings quality…and therefore we are concerned with the capital market consequences of earnings quality. Third, we view earnings quality as comprising both an innate, relatively stable component that is driven by factors intrinsic to business models and operating environments and a relatively more discretionary and fluctuating component that is driven by management’s financial reporting decisions.…” (Francis et al. 2008a, 261-2).

Hypotheses

Our first research hypothesis seeks to establish whether total BTDs are positively related to

cost of capital:

Hypothesis 1: Ceteris paribus, regardless of the form of BTD measures, firms with greater book-tax differences have higher cost of equity capital. Our second hypothesis focuses on information uncertainty, which reflects uncertainty about

the quality of firms’ earnings information and is the basis for expecting that we can derive an earnings

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quality measure from BTDs, and that such a measure is related to cost of capital. Our proxy for

information uncertainty is the component of BTDs that is not predicted by tax aggressiveness and firm

fundamentals (i.e., operating, investing, and financing activities, growth, and firm size) but captures

managerial discretion over financial reporting. Our second hypothesis is:

Hypothesis 2: Ceteris paribus, the greater the portion of firms’ book-tax differences not predicted by firm fundamentals and tax aggressiveness, the higher the firms’ cost of equity capital.

We test H1 by considering various BTD measures, and test H2 by modeling BTDs and

focusing on the portion not predicted by fundamentals and tax aggressiveness.

Cost of Equity Capital

There is an ongoing debate in the literature over several issues about cost of equity capital.

These include whether an ex ante or ex post measure of cost of capital is theoretically appropriate to

use (e.g., Francis et al. 2008b); whether firm-specific measures of cost of capital can be estimated

reliably (Easton 2006; Easton and Sommers 2007); and whether idiosyncratic risk as reflected in

proxies of information risk, such as accruals quality, is non-diversifiable and a priced risk factor

(Easley and O’Hara 2004; Francis et al. 2004 and 2005; Core et al. 2008; Francis et al. 2008a).

With regard to whether information risk is priced, the thrust of the relevant research has

focused on measures of earnings quality, especially accruals quality (e.g., Francis et al. 2005). Core

et al. (2008) re-examine Francis et al.’s (2005) analysis and raise questions as to whether accruals

quality is priced.6 However, accruals quality is only one way to capture uncertainty about earnings

quality, and even if it were definitively shown that accruals quality is not a priced risk component,

other measures of information uncertainty may exist and be related to cost of capital. Lambert et al.

(2007) demonstrate analytically that average precision of investors’ assessments of firms’ expected

6 Wysocki (2008) shows that accruals quality measures derived from variations of the Dechow and Dichev (2002) model exhibit weak and contradictory associations with other measures of accounting quality.

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cash flows, which captures their concept of information quality, is directly related to cost of capital.7

Bhattacharya et al. (2007) report empirical results that support that prediction with regard to earnings

quality measures and Ashbaugh-Skaife et al. (2009) do so concerning internal control deficiencies.

We view managerial discretion in financial reporting decisions as the key element of information

uncertainty, and investigate whether our proxy for information uncertainty is related to cost of capital.

Results demonstrating such a relation would be consistent with our BTD-based proxy of earnings

quality capturing measurement error in beta estimated from historical returns or with it being a priced

information risk factor.

Concerning empirical issues about cost of equity capital, there is no consensus in the literature

regarding the dominance of a particular approach for estimating cost of capital. Some studies use

realized security returns as a proxy for required returns, because ex ante required returns are not readily

available. However, Chen et al. (2008b), among others, argue against the use of ex post returns

because shocks to growth opportunities affect firms’ realized returns, and there is evidence that average

realized returns yield noisy measures of cost of equity capital (e.g., Elton 1999; Lakonishok 1993).8

We use ex ante (i.e., implied) measures of firm-specific risk premia in our primary analyses as we

believe they are theoretically more correct, but we also report results based on realized returns.

There are also issues regarding estimating firm-specific cost of capital. First, they are

estimated based on simplifying assumptions about expected long-term earnings growth beyond a short

forecast horizon, and Easton (2006) shows these assumptions measure investors’ expectations with

error. Second, they are estimated using analysts’ earnings forecasts, which Easton and Sommers

(2007) and others argue are optimistic and using them will yield upwardly biased cost of equity

7 Lambert et al. (2007) also show that information asymmetry has no effect on cost of capital after controlling for average precision. Also see Yee (2006).

8 Elton (1999) shows a low correlation between expected and realized returns and Lakonishok (1993) argues at least 70 years of stock return data are needed to show that market beta is a statistically significant risk factor. This suggests that ex post returns are unlikely to provide a powerful test of the relation between BTD variables and cost of capital.

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estimates. As a sensitivity check, we adopt the Easton and Sommers (2007) approach and use current

earnings realizations to estimate cost of capital and long-term growth rate simultaneously at the

portfolio level.

Our primary and most of our sensitivity analyses estimate cost of capital by relying on

Dhaliwal et al. (2006, 2007) and using the average of the four separate firm-specific ex ante cost of

capital estimates to minimize the impact that measurement error in any one of them would have (e.g.,

Hail and Leuz 2006; Dhaliwal et al. 2006). We also assess the sensitivity of the results by separately

considering the individual cost of capital measures.

III. RESEARCH DESIGN AND SAMPLE SELECTION

Research Design – Test of H1

We test Hypothesis 1 by regressing implied equity premium on the BTD variables and other

variables that can affect cost of equity capital. We use the following model:

Ravg_rf_it = α0 + α1 lnBMit + α2 LTGit + α3 lnDISPit + α4 lnMVEit + α5 βMKTit + α6 βSMBit

+ α7 βHMLit + α8 HiBTDit + α9 LoBTDit + α10 ABS_BTDit + α11 BTD_STDit

+ Σαj IndustryDummiesit + Σαk YearDummiesit + εit. (1)

The dependent variable (Ravg_rf) is firm i’s average implied equity premium, estimated using four

methods as of June of year t. The four ex ante cost of capital measures are attributable to: Gebhardt

et al. (2001), denoted as Rg_rf; Claus and Thomas (2001), denoted Rct_rf; Gode and Mohanram (2003),

denoted Roj_rf; and Easton (2004), denoted Rmpeg_rf. We discuss the various assumptions underlying

these measures in the Appendix.

For each cost of capital measure, we obtain the implied equity premium by subtracting the

yield on the 10-year Treasury note from the estimated cost of equity capital. Table 2 displays the

annual equity premium estimates generated by each of the four methods and the overall annual

averages, and also presents correlations over our sample period. The results indicate some substantial

differences in cost of estimates across the approaches, although the average of the four approaches is

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highly correlated with each of the four separate estimates (correlations range from 0.71 to 0.91).

Equation (1) includes several categories of control variables. First we consider variables

commonly identified as explaining cross-sectional differences in cost of capital. These include

properties of analyst forecasts using LTG, the mean analyst long-term growth forecast available in June

of year t, and lnDISP, the log of the standard deviation of analyst estimates of year t earnings divided

by the consensus forecast for year t earnings.9 We also adjust for sources of systematic risk, βMKT,

βSMB, and βHML, by estimating the Fama and French (1993) three-factor model in June of each year; we

obtain these factors for firms with at least 24 (and up to 60) months of stock return data ending in June

of year t. We control for firm-specific risk not captured by the Fama-French three factors (Dhaliwal

et al. 2006) using lnBM, the log of book value of equity divided by market value of equity at the

beginning of year t, and lnMVE, the log of market value of equity at the beginning of year t. Further,

we control for differences across industries and across years by including industry dummies, based on

Fama and French’s (1996) 48 industry classifications, and year dummies. Prior research (Gebhardt et

al. 2001; Gode and Mohanram 2003; Dhaliwal et al. 2006, 2007) suggests lnBM, LTG, lnDISP, and the

three factor loadings are positively related to cost of capital, while lnMVE is negatively related.

Our main interest in the test of H1 is with BTD variables, and our primary analysis considers

three sets of BTD variables: (i) HiBTD and LoBTD are indicator variables that equal 1 if BTD is,

respectively, in the largest or smallest quintile of the annual distributions of BTDs, which Hanlon

(2005) shows are informative about earnings persistence; (ii) ABS_BTD is the magnitude (i.e., absolute

value) of BTDs in year t; and (iii) BTD_STD is the standard deviation of BTDs calculated over years t-

4 through t. We expect a positive coefficient on each BTD variable. BTD equals pre-tax book

income minus taxable income, deflated by total assets. We estimate firm i’s taxable income by

grossing-up the current portion of its year t income tax expense by the federal statutory corporate tax

9 If the long-term growth forecast is not available, we use the log of the two-year-ahead earnings forecast divided by the one-year-ahead forecast minus one.

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rate.10, 11

Our panel data are subject to cross-sectional and time-series dependence problems. To

address this, we estimate equation (1) with regressions using two-way cluster-robust standard errors

clustered by both firm and time dimensions (Gow et al. 2008). To estimate these standard errors we

use the SAS code developed by Gow et al.12 Because this method does not allow for the inclusion of

fixed effects, we remove the industry and year effects in equation (1) by removing the industry mean

and annual mean from all dependent and independent variables before employing the method.13

Research Design – Test of H2

We derive our earnings quality measure by using an empirical model to predict BTDs as a

function of firm fundamentals and tax aggressiveness. We then focus on the unpredicted portion as

the basis for our information uncertainty proxy, which is the basis of our earnings quality measure, and

investigate whether it is related to cost of capital.

We derive our information uncertainty measure by modeling BTD as a function of

characteristics that capture firms’ operating, investing, and financing activities, growth, size, and tax

aggressiveness. Our model builds on prior research by Stickney and McGee (1982), Gupta and

10 As in prior research (e.g., Gleason and Mills 2002; Lev and Nissim 2004; Frank et al. 2009), the current portion of income tax expense is the sum of current federal (#63) and foreign income taxes (#64). If current foreign tax expense is missing on Compustat, we set it to zero. If current federal tax expense is missing, we set current portion of income tax expense to the difference between total and deferred tax expense. The top federal corporate tax rate was 46% for 1982-1986, 40% in 1987, 34% for 1988-1992, and 35% for 1993-2006.

11 We assess the extent of possible measurement error in estimating taxable income. We follow Lev and Nissim (2004) and rerun the analyses after excluding firms with relatively large amounts of foreign income (i.e., firm-years when the ratio of foreign-to-foreign plus domestic income exceeds 20 percent). Untabulated results are similar to the results for the full sample. Measurement error in estimating taxable income also might arise because we ignore the R&D tax credit. Following Hanlon et al. (2005), we rerun our analyses excluding high R&D intensive firm-years (i.e., R&D/Sales exceeds 5%). Our inferences are unchanged. 12 We obtained the SAS code from the following website: http://www.stanford.edu/~igow/GOT/. 13 Petersen (2008) demonstrates that in the simultaneous presence of a possible firm effect (residuals of a given firm correlated across years) and a time effect (residuals of a given time correlated across firms), OLS standard errors, Newey-West (1987) corrected standard errors, White standard errors, and standard errors obtained using the Fama and MacBeth (1973) approach can be biased. Petersen suggests clustering on two dimensions simultaneously (e.g., firm and time), which allows for correlations among different years for the same firm and different firms in the same year.

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Newberry (1997), and Frank et al. (2009). The model is:

BTDit = β0 + β1 SIZEit + β2 LEVit + β3 CAPINTit + β4 INVINTit + β5 RDINTit

+ β6 ROAit + β7 GROWTHit + β8 FORRATIOit + β9 DTAXit + εit. (2)

As above, BTD is firm i’s year t book-tax differences. Equation (2) includes independent

variables that reflect a firm’s economic fundamentals and tax-related variables expected to be useful in

predicting BTD. More specifically, the regressors capture the following: (i) investment and asset

mix using capital intensity, CAPINT (net property, plant, and equipment scaled by total assets),

inventory intensity, INVINT (inventory scaled by total assets),14 and R&D intensity, RDINT (research

and development (R&D) expense scaled by net sales); (ii) financing and capital structure using

leverage, LEV (long-term debt scaled by total assets); (iii) firm performance using return on assets,

ROA (pre-tax income divided by total assets)15; (iv) firm size and growth using SIZE (the log of total

assets) and GROWTH (change in total assets scaled by the prior year’s total assets); and (v) tax-related

variables using extent of foreign income, FORRATIO (ratio of foreign sourced pre-tax income to total

pre-tax book income), a proxy for tax complexity, and tax aggressiveness, DTAX, which Frank et al.

(2009) show dominates other tax aggressiveness proxies. DTAX reflects discretionary permanent

BTDs and is based on the residuals from a model estimated by regressing total permanent differences

(total BTDs less temporary BTDs) on statutory adjustments (e.g., state taxes) and nondiscretionary

items known to cause permanent differences (e.g., intangible assets) but not likely related to tax

reporting aggressiveness (see Frank et al., 2009, for additional details).

We estimate equation (2) for the Fama-French 48 industry groups annually to obtain firm-

specific values of the predicted and unpredicted components of BTD. Predicted values from equation

(2) yield an estimate of the portion of BTD that firm i’s fundamentals and tax aggressiveness predict,

14 We adjust inventory for any LIFO reserve balance. While similarly affecting INVINT’s numerator and denominator, it changes the value of the ratio and thus can affect the regression results.

15 We obtain virtually identical results when defining ROA based on operating income and when using ROE.

15

denoted as EXP_BTD. Then, annual cross-sectional estimation of equation (2) yields firm- and year-

specific residuals that represent the portion of BTD not predicted by the model. The residuals proxy

for uncertainty about earnings and reflect the portion of BTDs due to managerial discretion over

financial reporting.16 We consider two forms of the financial reporting information uncertainty

variable: the absolute value of the residuals (ABS_IU) and the standard deviation of the residuals

(IU_STD) estimated over years t-4 through t.17

We test Hypothesis 2 using equation (3), which regresses Ravg_rf, firm i’s average implied

equity premium in June of year t, on EXP_BTD, EXP_BTD_STD, IU_STD, ABS_IU, and the control

variables from equation (1).18 Equation (3) is:

Ravg_rf_it = α0 + α1 lnBMit + α2 LTGit + α3 lnDISPit + α4 lnMVEit + α5 βMKTit + α6 βSMBit

+ α7 βHMLit + α8 EXP_BTDit + α8 EXP_BTD_STDit + α10 ABS_IUit + α11 IU_STD

+ Σαj IndustryDummiesit + Σαk YearDummiesit + εit. (3)

Our analysis is based on two-way cluster-robust standard errors that are clustered by both firm and

time dimensions, which is the same approach we use to estimate equation (1).

H2 predicts the coefficient on ABS_IU and IU_STD will be positive (i.e., cost of capital is

increasing in our proxy for information uncertainty). Based on the residuals from equation (2),

ABS_IU and IU_STD reflect BTDs beyond fundamentals and tax aggressiveness and capture

information uncertainty due to managerial discretion over financial reporting. We interpret the

coefficients on ABS_IU and IU_STD as indicating the strength and direction of the relation between

16 Our approach is consistent with that used by Francis et al. (2005) who examine earnings quality variables and refer to their innate and discretionary components.

17 We model DTE using equation (2) but after dropping DTAX. First, DTAX is based on the difference between total BTDs and DTE and thus is mechanically related to DTE. Second, DTAX reflects discretionary permanent differences. BTDs include permanent differences whereas DTE does not. 18 Since IU_STD reflects greater variability than the expected level of BTD, we include EXP_BTD_STD, the standard deviation of EXP_BTD over time, in addition to including EXP_BTD, as a regressor in equation (3) to ensure that the importance of the expected level of BTD is not swamped by IU_STD.

16

cost of capital and our information uncertainty-based measure of earnings quality.

Sample Selection

We analyze observations from the period 1982 to 2006.19 We begin with a sample of firm-

years in the Compustat database that have nonmissing asset data over the period 1978 through 2006.20

We drop (a) financial institutions and utilities, due to the high degree of regulation and tax rules

specific to these industries; and (b) foreign firms, due to a limited ability to estimate taxable income

because of different rules across tax jurisdictions and because of different financial reporting regimes.

We require firms to have five consecutive years of book and taxable income data to compute

BTD_STD and IU_STD, and also require the following: one-year- and two-year-ahead earnings

forecasts, a forecast of long-term earnings growth, and stock price data, all from I/B/E/S; book value of

equity and dividend data from Compustat; and sufficient stock return data from CRSP to calculate the

Fama-French three factors.21 We winsorize all continuous variables at the top and bottom 1% of

distributions to mitigate the effect of extreme values. The final sample contains 20,687 firm-years to

test H1 and 12,997 firm-years to test H2. The sample used to test H2 is smaller primarily due to the

need to estimate the tax aggressiveness variable (see Table 1).

IV. RESULTS

Descriptive Statistics

Table 2 reports annual sample sizes, the cross-sectional annual mean estimates of the implied

equity premium for Ravg_rf (i.e., the average of the four alternative firm-specific cost of capital

estimates) and for each of the four cost of capital estimates, Rg_rf, Rct_rf, Roj_rf, and Rmpeg_rf, as well as

19 I/B/E/S forecasts of long-term growth in earnings per share are available only since 1982.

20 Sample selection begins in 1978 since we compute the standard deviation of BTDs over five-year periods. 21 Firms must have three-year-, four-year-, and five-year-ahead earnings forecasts or an earnings growth estimate to calculate the Claus and Thomas cost of capital. Firms must have positive one-year- and two-year-ahead earnings forecasts for the Gode and Mohanram and the Easton measures of cost of capital.

17

means across all 25 sample years for each estimate. The overall mean Ravg_rf is 4.96%, and the four

individual estimated equity premiums range from an average of 3.09% for Rg_rf to 6.20% for Roj_rf.

The four measures of implied equity risk premia are reasonably close to those reported over different

sample periods in prior research.22 Also consistent with recent research (e.g., Botosan and Plumlee

2005; Guay et al. 2005; Dhaliwal et al. 2006), Rmpeg_rf and Roj_rf yield the largest equity risk premium

estimates, whereas Rg_rf produces the smallest.

Summary statistics and correlations for regression variables are in Table 3. Panel A indicates

the mean firm-year BTD over the sample period is 0.0155, or about 1.6% of total assets (median =

0.0174), mean ABS_BTD is 0.0384 (median = 0.0270), and mean standard deviation of BTDs over

time (BTD_STD) is 0.0412 (median = 0.0251). Regarding control variables, mean MVE is $3.63

billion, mean BM is 52.4%, mean dispersion in analysts’ forecasts (DISP) is 11.2%, mean forecasted

long-term annual earnings growth rate (LTG) is 16.2%, and mean market beta is 1.10. Since the

medians for MVE, BM, and DISP are substantially below their respective means, which suggests

marked skewness in the data, we include these variables in log form in equations (1) and (3).

Pearson and Spearman correlations in Panel B indicate that the BTD variables are pair-wise

positively correlated with the exception of HiBTD and Lo BTD, which as expected are negatively

related. Ravg_rf is positively related to BTD_STD across all firm-years, whereas Ravg_rf is positively

related to ABS_BTD only for the Pearson correlation. Ravg_rf is positively related to LoBTD, but

surprisingly negatively related to HiBTD for both Pearson and Spearman correlations. A negative

correlation between Ravg_rf and any BTD variable is counter to expectations, although this is not a

multivariate analysis.

22 The average annual mean of equity premium reported by Gebhardt et al. (2001) is 2.7% (1979-1995) while Rg_rf in our sample (1982-2006) is 3.09%. The mean equity premium in Claus and Thomas (2001) is 3.4% (1985-1998) while Rct_rf is 4.34% in our sample. The mean equity premium in Gode and Mohanram (2003) is 5.6% (1984-1998) while Roj_rf is 6.20% in our sample. Finally, the mean equity premium in Easton (2004) is approximately 4.0% (1981-1999) while Rmpeg_rf is 6.19% in our sample.

18

Results of the Test of Hypothesis 1

Table 4 displays the results of estimating four versions of equation (1) to test H1, the

hypothesized positive relation between BTD variables and cost of capital. Each regression includes

the control variables and various BTD variables.

The first regression, shown in column (1), includes the 0/1 variables that indicate the presence

of high and low extreme values of BTD (i.e., HiBTD and LoBTD), and the coefficient on each is

positive and significant at the 1% level. Column (2) includes only ABS_BTD, and its coefficient is

also significantly positive (1% level), and Column (3) indicates that when we include only BTD_STD

in the model it too has a significant and positive coefficient (1% level). Column (4) reports results

when all of the BTD variables are included in the same model. The coefficients on BTD_STD and

LoBTD continue to be positive and significant (1% level), as does the coefficient on ABS_BTD (5%

level), but the coefficient on HiBTD is insignificant. Thus, BTD_STD, LoBTD, and ABS_BTD each

consistently have significantly positive associations with cost of capital, but this is not the case for

HiBTD.23, 24

We re-do the analysis by replacing the BTD variables with corresponding versions of deferred

tax expense, DTE (results are untabulated and based on a sample of 13,234 firm-years). First, the

23 Using individual cost of capital estimates yield results generally consistent with those based on averaging across the four separate cost of capital measures (untabulated). For example, when all BTD variables are in the same model, BTD_STD is positive and is significant for three of the four cost of capital measures; ABS_BTD is positive and significant for two of four measures; LoBTD is positive and significant for two measures but reliably negative for one measure; and HiBTD is positive and significant for one measure.

24 Results of additional analyses (untabulated): (i) Using variable ranks yields qualitatively similar results. (ii) Following Lev and Nissim (2004) and Weber (2009), we include the decile ranking of the ratio taxable income-to-income before extraordinary items, and find its coefficient is reliably negative. When we include all BTD variables including the tax-book ratio rank variable in the same model, the coefficient on the tax-book ratio remains reliably negative and only BTD_STD and LoBTD have positive and significant coefficients. (iii) We include changes in BTD (chgBTD). When it is the only BTD variable in the regression, chgBTD has a reliably negative coefficient; its coefficient becomes insignificant when chgBTD is included in the same regression with the other BTD variables. (iv) We include BTD instead of HiBTD and LoBTD, and its coefficient is consistently negative. (v) We replace BTD and ABS_BTD with, respectively, the mean of BTDs (MEAN_BTD) computed over the same 5-year periods we estimate BTD_STD and the absolute value of the mean of BTDs (ABS_MEAN), and re-estimate equation (1). We obtain similar results to those in Table 4, which suggests that the significance of the coefficient on BTD_STD is not due simply to an over-time BTD effect, but rather to an over-time variability BTD effect.

19

Pearson (Spearman) correlation between BTD and DTE is 0.565 (0.714). Second, we obtain results

entirely consistent with those in columns (1), (2), and (3) of Table 4 for the DTE variables. Third,

when we include all of the DTE variables in the same model, the coefficient on the standard deviation

of DTE over time is positive and significant, and so too are the coefficients on both high and low

values of DTE; this latter result extends Hanlon’s (2005) findings to cost of equity capital. The

coefficient on the absolute value of DTE is insignificant. Overall, the results indicate that BTD-

related (and DTE-related) variables are generally positively related to cost of capital.

The signs on the control variable coefficients are generally as expected. Across all four

regressions in Table 4, lnBM, LTG, lnDISP, and the three Fama-French risk factors each have positive

coefficients, lnMVE has a negative coefficient, and all coefficients are consistently significant except

for the coefficients on βSMB and βMKT. When estimating equation (1) using DTE variables, all of the

control variables have significant coefficients.

Results of the Test of Hypothesis 2

We first present the results of estimating equation (2), the BTD model from which we obtain

the information uncertainty variables. This is followed by the results for H2.

We estimate equation (2) on an industry-year basis for each of the Fama and French (1996) 48

industry groups, excluding utilities and financial institutions. We require at least 15 firms for each

industry-year, with each firm having data for all variables in equation (2) for a given year.25 Table 5

displays summary statistics and correlations for the pooled sample of 75,315 firm-years.

Descriptive results for equation (2) variables indicate that BTD has a mean (median) of -

0.0693 (0.0088), as compared to a mean (median) of 0.0155 (0,0174) in the sample we use to test H1,

which is almost 60% larger than the sample we use to test H2 due to the need to compute the tax

aggressiveness variable for equation (2). Mean and median DTAX is close to zero, as in Frank et al.

25 Using two-digit SIC industry groups does not change the results.

20

(2009), and mean ROA is slightly negative while its median is positive.26 Regarding correlations,

BTD is significantly related to each independent variable. In addition, there are significant

associations between several independent variables, although none exceeds 0.41. While this raises

the possibility of multicollinearity, it is not a major concern here since the purpose of equation (2) is

not to test the importance of individual explanatory variables of BTD, but rather to predict BTD and

use the residuals from the prediction model to proxy for information uncertainty, the basis for our

earnings quality measure.

Table 6 presents the results of estimating equation (2) by showing the mean coefficients across

the industry-year regressions. The regression has an adjusted R2 of 76%. All of the independent

variables except RDINT have significant coefficients and the results suggest that BTD is positively

related to firm fundamentals for capital and inventory intensity, leverage, profitability, size, and growth,

and also tax aggressiveness, and negatively related to the extent of foreign source income.27

Descriptive statistics for the variables derived from equation (2) that we include in equation

(3) to test H2 are presented at the bottom of Table 3, Panel A. For the pooled sample of observations,

the means of EXP_BTD and EXP_BTD_STD are, respectively, 0.0246 and 0.0442; mean IU is -0.0096,

and the means of ABS_IU and IU_STD are, respectively, 0.0420 and 0.0409. Median values are

slightly less for each variable. Panel B indicates that Ravg_rf is negatively (positively) associated with

EXP_BTD (EXP_BTD_STD) and negatively (positively) associated with ABS_IU (IU and IU_STD).

The results of testing H2 are shown in Table 7 and we report three versions of equation (3).

In addition to control variables, Column (1) includes only ABS_IU, column (2) only IU_STD, and

26 Descriptive statistics based on the Compustat population for the same time period follow: BTD (mean = -0.105, median = 0.003); ROA (mean = -0.038, median = 0.046); and SIZE (mean = 4.251, median = 4.176).

27 We replace BTD with DTE (untabulated) and find: (i) DTE is significantly correlated with each independent variable included equation (2). (ii) Significant results from estimating the modified equation (2) (see footnote 18) indicate that DTE is positively related to capital intensity, leverage, profitability, and growth, and negatively related to investment and R&D intensities, with ROA and CAPINT being the most significant variables. The model’s adjusted R2 is 9.4%.

21

column (3) both ABS_STD and IU_STD. First, we obtain similar results for the control variables as

we find when estimating equation (1) in Table 4; the only change is that the coefficient on βMKT is now

significant in all three regressions. Second, the coefficient on EXP_BTD is never significant, but the

coefficient on EXP_BTD_STD is positive and significant (p-value = 0.04). Turning to the main

variables of interest in testing H2, we find that the coefficients on ABS_IU and IU_STD are positive

and significant when each is the only information uncertainty proxy in the model. However, when

both variables are included in the same regression, only the coefficient on IU_STD is positive and

significant (p-value = 0.09).28

Untabulated results of estimating equation (3) based on DTE variables are highly consistent

with those reported in Table 7. Both DTE versions of the IU variables (denoted ABS_IU_DTE and

IU_STD_DTE) have positive and significant coefficients when each is the only information uncertainty

variable in the model, but when they are in the same only IU_STD_DTE is significant (p-value = 0.01).

In additional, both EXP_DTE (p-value = 0.05) and EXP_DTE_STD (p-value = 0.01) have positive and

significant coefficients.

Hence, the results suggest the unpredicted component of variability in BTDs (and DTE) over

time, which reflects information uncertainty due to managerial discretion over the financial reporting

process and is our earnings quality measure, is related to cost of capital. Because IU_STD (and

IU_STD_DTE) is significant beyond our estimate of historical market beta, the results are consistent

with Lambert et al.’s (2007) model and suggest that our earnings quality variable captures information

effects related to cost of capital. In addition, since we control for other risk factors, the results are

also consistent with IU_STD (and IU_STD_DTE) being an information risk factor.

28 Results of testing H2 using the separate cost of capital estimates, instead of averaging across the four measures, are consistent with the main results. For example, with both ABS_IU and IU_STD in the same model, the coefficient on IU_STD is positively significant for three of the four cost of capital estimates whereas the coefficient on ABS_IU is positively significant for only one measure.

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Sensitivity Analyses of Tests of H1 and H2

We assess the robustness of our results by conducting a series of sensitivity checks.

Institutional Holdings and Earnings Quality Variables. We consider the impact of

institutional ownership and earnings quality variables identified in prior research on the tests of H1 and

H2. First, if institutional investors serve as effective external monitors of management and the

alignment of managers’ and shareholders’ interests, then we expect that greater institutional holding is

related to lower opportunistic managerial discretion over financial reporting, and our BTD differences

are more likely to be driven by fundamental factors than managerial discretion of accounting choice.

We test this conjecture by augmenting equations (1) and (3) with HIGH (an indicator variable that

equals one if institutional ownership of a firm’s shares is above the sample median, and zero

otherwise) and the interaction of HIGH with the BTD variables and information uncertainty variables.

We expect that the coefficient on the interaction terms will be negative and significant in the presence

of a high level of institutional holdings.

Second, as noted above prior research (e.g., Francis et al. 2005) investigates a link between

accruals quality and other earnings quality measures and cost of capital. We estimate AQ, the

standard deviation of residuals from annual cross-sectional estimations (years t-4 to t) using the

McNichols (2002) model,29 and also consider SMOOTH (standard deviation of income before

extraordinary items/standard deviation of operating cash flows), abs_AA (absolute value of

performance-adjusted modified Jones model abnormal accruals), and PERSIS (firm-specific time-

series earnings persistence over 10-years). Higher values of AQ, SMOOTH, and abs_AA and lower

values of PERSIS reflect lower earnings quality. We control for these earnings quality variables to

ensure they are not driving our results.

Panels A and B of Table 8 display the results of incorporating institutional holdings and

29 McNichols (2002) augments Dechow and Dichev’s (2002) accruals quality model with the Jones (1991) abnormal accruals model.

23

alternative earnings quality variables into the tests of H1 and H2. In Panel A, we report four sets of

results for H1. First, the results for the BTD variables when considered separately in columns (1)-(3)

are very similar to those for our main tests shown in Table 4. Second, HIGH is consistently positive

and significant and its interaction with each of the BTD variables when considered separately is

negative, as expected; this is consistent with high institutional ownership mitigating the positive

relation between the BTD variables and cost of capital. Third, all of the earnings quality variables

from prior research are significantly related to cost of capital in the expected direction. Fourth, the

results in column (4), when all of the variables are in the model, reveal that the coefficients on

BTD_STD and LoBTD are significant and positive at the 1% and 5% levels, respectively. Hence,

BTD_STD and LoBTD impact cost of capital incrementally to the impact of institutional ownership and

to earnings quality variables identified in prior research.

The results for the impact on H2 of institutional ownership and alternative earnings quality

variables are shown in Panel B of Table 8. First, HIGH is positive and significant when IU_STD is in

the model, and the interactions of HIGH with ABS_IU and IU_STD in columns (1) and (2),

respectively, have negative and significant coefficients, consistent with high institutional ownership

dampening the effect on cost of capital of greater information uncertainty. Second, we find in

untabulated results that IU_STD is correlated with quality variables in the expected manner: AQ (r =

0.52), SMOOTH (r = 0.28), and abs_AA (r = 0.22), and PERSIS (r = -0.10). In the multivariate

analysis in Panel B only AQ and SMOOTH have positive and significant coefficients. More

importantly, when we include all variables in the same model, IU_STD continues to have a positive

and significant coefficient. Hence, after controlling for the impact of institutional holdings and

alternative earnings quality variables, our inferences regarding H1 and H2 continue to hold.

Analysts’ Earnings Forecasts Bias. Our cost of capital measures rely on analysts’ forecasts,

and there is a concern that differences in forecasting behavior can affect the results. To the extent that

earnings forecasts tend to be optimistic but investors understand this bias and properly adjust prices,

24

then implied cost of capital models will yield upwardly biased estimates (Botosan and Plumlee 2005;

Hail and Leuz 2006). We control for this potential bias by including analyst forecast errors (FERR) in

equations (1) and (3). FERR is the difference between one-year-ahead analysts’ mean consensus

forecasts and actual earnings, scaled by end-of-fiscal-year stock price. If forecasts tend to be

optimistic, FERR assumes positive values. We thus expect a positive coefficient on FERR if markets

back-out the bias, and we find this in untabulated results. With regard to H1, we find that the

coefficients on the BTD variables are all positive and significant when separately included in the

regression. When we include all BTD variables in the same model BTD_STD and LoBTD are

positive and significant at the 5% level while both HiBTD and ABS_BTD have insignificant

coefficients.30 For H2, we obtain results similar to our main analysis. The coefficients on ABS_IU

and IU_STD are significantly positive when considered individually but only IU_STD is significant

when both variables are in the regression. Thus, our results are not driven by biases due to

differences in analyst forecasting behavior.

Simultaneous Estimation of the Cost of Equity and Growth Rate. Estimated firm-specific

implied costs of capital (Gebhardt et al. 2001, Claus and Thomas 2001, Gode and Mohanram 2003,

and Easton 2004) rely on simplifying assumptions about the rate of expected long-term earnings

growth. Easton (2006) demonstrates that these assumptions measure investors’ expectations of long-

term growth with error. As an alternative, Easton simultaneously estimates cost of capital and

expected long-term growth rate for stock portfolios to avoid the error that can arise when assuming an

expected growth rate. Moreover, another weakness of using firm-specific implied costs of capital,

alluded to above, is that it is estimated by using analysts’ forecasts. Easton and Sommers (2007)

argue that to the extent analysts’ forecasts are optimistic, using them yields upwardly biased estimates

30 The Pearson correlations between FERR and each of the BTD variables are below 0.04 in all cases.

25

of cost of equity, which could lead to the erroneous conclusions.31

Hence, as another sensitivity check, we adopt the Easton and Sommers (2007) method of

portfolio-specific estimates of cost of equity and use current earnings realizations in place of analysts’

forecasts to estimate cost of capital simultaneously with the long-term growth rate. One difficulty in

estimating portfolio-specific cost of capital is controlling for factors that may affect implied cost of

capital. We follow Chen et al. (2008b) and first sort our sample based on market beta, size (lnMVE),

and book-to-market ratio (lnBM) into three groups for each of the three factors at the end of each year

over 1982-2006. We obtain 675 portfolios (i.e., 3×3×3×25) and estimate cost of capital in each

portfolio. We then determine median values for independent variables in each portfolio, and examine

the relation between cost of capital and median values of the BTD variables:

RES_ rf_pt = α0 + α1 lnBM_Medianpt + α2 lnMVE_Medianpt + α3 βMKT_Medianpt

+ α4 βSMB _Medianpt + α5 βHML_Medianpt + α6 HiBTD_Medianpt

+ α7 LoBTD_Medianpt +α8 ABS_BTD_Medianpt + α9 BTD_STD_Medianpt + εpt (4)

RES_rf_pt = α0 + α1 lnBM_Medianpt + α2 lnMVE_Medianpt + α3 βMKT_Medianpt + α4 βSMB _Medianpt

+ α5 βHML_Medianpt + α6 EXP_BTD_Medianpt + α7 EXP_BTD_STD_Medianpt

+ α7 ABS_IU_Medianpt + α8 IU_STD_Medianpt + εpt (5)

where RES_rf_pt is the implied cost of capital estimated following Easton and Sommers (2007) for

portfolio p in year t minus the yield on the 10-year Treasury note in year t; and all other independent

variables are median values of variables previously defined.

Table 9 reports the results of estimating equations (4) and (5) to validate our main results.

For H1, the coefficients on LoBTD_Median and ABS_BTD_Median are significantly positive at the

10% level whereas the coefficient on BTD_STD_Median is significantly positive at the 1% level when

all of the BTD variables are in the same model in column (4). For H2, the results in column (7)

31 McInnis (2008) shows that evidence of a link between smoother earnings and lower implied cost of capital is driven primarily by optimism in analysts’ long-term earnings forecasts.

26

indicate that, in contrast to the results in Table 7, the coefficient on EXP_BTD_STD_Median is

insignificant while the coefficient on ABS_IU_Median is positive and significant (10% level).

Consistent with Table 7’s results, the coefficient on IU_STD_Median is positive and significant (5%

level). Thus, results using a portfolio approach to estimating cost of capital generally confirms the

significance of our BTD-derived earnings quality variable, consistent with the results of the primary

analysis that is based on firm-specific estimates of implied cost of capital.

Ex Post Returns as a Proxy for Cost of Equity. While implied cost of capital is the

theoretically correct measure to use in our analysis, we also report results based on realized stock

returns. That is, instead of using implied cost of capital as the dependent variable, we estimate

equations (1) and (3) using ex post stock returns, defined as the annual return for year t minus the yield

on 10-year Treasury note (Expost_rf). The annual return is the buy-and-hold return of the security

compounded from the fourth month after the end of fiscal year t, which allows for dissemination of

firms’ annual Form 10K reports.

Untabulated results for the four variations of equation (1) reported in Table 4 reveal the

coefficients on BTD_STD are always positive and significant (5% level). Coefficients on HiBTD and

LoBTD are insignificant across all four regressions, while coefficients on ABS_BTD are reliably

negatively related to Expost_rf, contrary to expectations. The weaker results reported here are

consistent with ex post returns being a poorer proxy for implied cost of capital. For H2, both ABS_IU

and IU_STD are positive but insignificant.

V. CONCLUSION

We investigate whether differences between book and taxable incomes explain differences in

cost of equity capital across firms. Prior research suggests that BTDs reflect firms’ earnings

management, tax planning, and underlying economic fundamentals, including some aspects of risk,

and we conjecture that BTDs capture information uncertainty with regard to managerial discretion over

accounting choices and posit a positive relation between BTDs and cost of capital. Our research

27

contributes to the literature by providing a deeper understanding of the information captured by

differences between these two measures of firm performance.

The results indicate that BTDs are positively and significantly related to cost of capital, with

the relation between standard deviation of BTDs over time and cost of capital being positive and most

significant among the BTD variables. We develop and estimate a model to predict BTDs and focus

on the residuals, the portion not predicted by firm fundamentals and tax aggressiveness, which we

interpret as capturing information uncertainty due to managerial discretion over financial reporting.

The standard deviation of the residuals over time is our earnings quality measure, and it is strongly

positively related to cost of capital. The results are robust to replacing total BTDs with temporary

BTDs (i.e., deferred tax expense) and with several sensitivity checks, including considering the impact

of institutional holdings and alternative earnings quality measures that are derived solely from book

income and estimating cost of capital at the portfolio level.

Viewed within the framework provided by the CAPM-based model developed by Lambert et

al. (2007), our research examines whether our BTD-derived earnings quality measure reflects

information effects that are related to cost of capital, which would be consistent with empirical

estimates of beta based on historical returns not fully capturing information effects. If the possibility

of multiple risk factors is allowed (e.g., Indjejikian 2007), then our investigation can be viewed as an

attempt to separately identify firm innate characteristics and discretionary information effects and

contributes to the literature that seeks to determine whether there is an “information risk factor” (e.g.,

Francis et al. 2004; Ashbaugh-Skaife et al.2009). Our results are consistent with both views.

28

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32

APPENDIX: Cost of Equity Capital Measures

Gebhardt et al. (2001) estimate a residual income model using analyst earnings

forecasts in years t+1 and t+2, long-term growth forecasts for year t+3 earnings, and terminal

value estimates. Earnings forecasts beyond year 3 are estimated assuming the year t+3 return

on equity (ROE) reverts to the industry median ROE by year t+T (T=12).

TVBr

rFROEB

r

rFROEBP t

g

gtt

g

gttt

12

21

)1()1(, where FROEt+i is forecasted ROE in

period t+i and equals FEPSt+i/Bt+i-1 for years 1-3, and Bt+i is year t+i book value of equity

divided by the number of common shares outstanding in June of year t+i. Using clean surplus

accounting, Bt+i = Bt+i-1 + FEPSt+I×(1-k). FEPS is forecasted earnings per share and FEPS1

and FEPS2 equal the 1-year- and 2-year-ahead consensus EPS forecasts in I/B/E/S in June of

year t. FEPS3 equals the 3-year-ahead EPS forecast, if available; otherwise FEPS3 is

FEPS2×(1+long-term growth forecast). k is expected dividend payout ratio (dividends per

share divided by earnings per share in year t-1). If EPS ≤ 0, then k equals 6% of total assets

at the beginning of year t. TV, the terminal value, is calculated as:

111

1

3 )1()1(

TtT

gg

gTtit

T

ii

g

git Brr

rFROEB

r

rFROETV .

Claus and Thomas (2001) use the following residual income model:

55

55

44

33

221

00 )1)((

)1(

)1()1()1()1()1( ctctctctctctct rgr

gae

r

ae

r

ae

r

ae

r

ae

r

aeBP

.

aet is year t expected abnormal earnings equal to FEPSt - rct×Bt-1. For years 3-5, FEPSt+i

equals the consensus EPS forecast, if available; otherwise FEPSt+i = FEPSt+i-1×(1+long-term

growth forecast). Bt+i equals Bt+i-1 + k×FEPSt+i, assuming k=0.5. g, the growth in abnormal

earnings beyond t+5, equals the yield on the 10-year Treasury note minus 3%.

33

Gode and Mohanram (2003) use a model based on Ohlson and Juettner-Narouth (2005):

))03.0((1

2

ft

toj rg

P

EPSAAr

where ),)03.0((5.0 1

t

tf P

DPSrA

,)(

1

12

t

tt

FEPS

FEPSFEPSg

rf = yield on a 10-year

Treasury note, and DPS = dividends per share (DPSt+1 = DPS0). This model assumes that g

(short-term growth) decays asymptotically to a perpetual growth rate (rf – 0.03) and requires

that FEPSt+1 and FEPSt+2 be positive.

Easton (2004) uses a modified PEG ratio (PE ratio divided by the short-term rate of

earnings growth, modified to include expected dividends in the estimate of short-term growth):

,)(

2

1120

mpeg

ttmpegt

r

EPSDPSrEPSP

where EPS2 ≥ EPS1 > 0 and DPSt+1 = DPS0. This

model constrains EPS2 ≥ EPS1 > 0 so the solution has two real roots, one of which is positive.

Easton and Sommers (2007) use current earnings realizations instead of analysts’

earnings forecasts and estimate cost of capital simultaneously with the expected growth rate.

Their residual income valuation model is adapted from O’Hanlon and Steele (2000):

)(

)1()(

_

1_

gr

gBPSrEPSBPSP

es

testtt

where BPSt = book value of equity per share, EPSt = current earnings per share, and g =

perpetual growth rate. Easton and Sommers (2007) transform this equation to form:

,)(

110

1jt

jt

jtjt

jt

jt

BPS

BPSP

BPS

EPS

where δ0 = r_es and δ1 = (r_es - g)/(1 + g). δ0 and δ1 are simultaneously estimated and thus r_es

= δ0 and g = (δ0 - δ1)/(1 + δ1).

34

Table 1 Sample Selection

Sample Selection for H1 Initial sample with necessary data available in Compustat (1978-2006) 149,727 less utilities and financial institutions (29,427) less foreign firms (8,653)

Remaining sample 111,647 less observations with missing BTD (9,611) less observations with missing BTD_STD (42,174)

Remaining sample 59,862 less observations with missing Ravg_rf (36,593) less observations with missing other control variables (lnDisp, lnBM, LTG, and lnMVE) (2,582)

Final Sample (1982-2006) for H1 20,687

Sample Selection for H2 Initial sample with necessary data available in Compustat (1978-2006) 149,727 less utilities and financial institutions (29,427) less foreign firms (8,653) Remaining sample 111,647 less observations with missing variables for computing tax aggressiveness (32,602) less observations with less than 15 observations in each industry-year (2,069) Remaining sample 76,976 less observations with missing variables for computing IU (1,648) less observations with less than 15 observations in each industry-year (13) less observations with missing IU_STD (36,386) less observations with missing Ravg_rf (24,409) less observations with missing other control variables (lnDisp, lnBM, LTG, and lnMVE) (1,523) Final Sample (1982-2006) for H2 12,997

35

Table 2 Cost of Equity Estimates and Correlations

Panel A: Annual average of cost of equity premiums (N=20,687)

Year N Ravg Rg Rct Roj Rmpeg

1982 513 4.89% 0.99% 5.38% 6.88% 6.33%

1983 548 3.93% 0.69% 2.33% 6.76% 5.92%

1984 638 3.34% -0.74% 4.04% 5.65% 4.41%

1985 623 4.37% 1.93% 4.18% 6.09% 5.30%

1986 619 4.46% 2.58% 3.46% 6.04% 5.74%

1987 672 3.95% 1.65% 3.02% 5.70% 5.45%

1988 637 3.82% 2.01% 3.86% 5.13% 4.28%

1989 644 3.92% 2.30% 4.03% 5.06% 4.29%

1990 705 4.28% 2.02% 4.20% 5.61% 5.29%

1991 765 4.43% 2.12% 3.61% 6.00% 5.99%

1992 796 5.45% 2.71% 4.67% 7.00% 7.43%

1993 821 5.57% 3.44% 4.68% 6.88% 7.28%

1994 876 4.68% 2.26% 4.40% 6.06% 6.00%

1995 908 5.43% 3.45% 4.99% 6.61% 6.65%

1996 984 4.34% 2.34% 4.00% 5.61% 5.40%

1997 1058 4.54% 2.70% 4.15% 5.73% 5.59%

1998 1060 5.46% 3.69% 4.87% 6.52% 6.76%

1999 1060 5.25% 3.66% 4.72% 6.25% 6.38%

2000 1015 6.00% 4.18% 6.13% 6.83% 6.86%

2001 867 5.55% 4.39% 4.55% 6.47% 6.79%

2002 875 5.52% 4.15% 4.16% 6.55% 7.23%

2003 897 6.67% 6.21% 5.00% 7.24% 8.22%

2004 1037 5.06% 4.17% 3.76% 5.92% 6.39%

2005 1044 5.48% 4.83% 4.25% 6.21% 6.64%

2006 1025 5.04% 4.03% 4.35% 5.83% 5.95%

Mean 4.96% 3.09% 4.34% 6.20% 6.19%

Panel B: Pearson correlation coefficients between cost of equity estimates Ravg_rf Rg_rf Rct_rf Rmpeg_rf Roj_rf

Ravg_rf 1.0000 0.7190 0.7057 0.8899 0.9120

Rg_rf 1.0000 0.4703 0.5031 0.4907

Rct_rf 1.0000 0.3602 0.4541

Rmpeg_rf 1.0000 0.9502

Roj_rf 1.0000 * All correlation coefficients are significant at the 0.0001 level. Ravg_rf is the implied cost of equity capital for firm i in June of year t minus the year t yield on a 10-year U.S. Treasury note. Ravg_rf is the average of four implied equity premia: Rg_rf, the implied equity premium measured by Gebhardt et al. (2001); Rct_rf, the implied equity premium measured by Claus and Thomas (2001); Roj_rf, the implied equity premium measured by Gode and Mohanram (2003); and Rmpeg_rf, the implied equity premium measured by Easton (2004). See the Appendix for details.

36

Table 3 Summary Statistics and Correlations

Panel A: Summary statistics

N Mean Std. Dev. Q1 Median Q3

Ravg_rf 20687 0.0496 0.0297 0.0306 0.0449 0.0629

BM 20687 0.5241 0.3213 0.2993 0.4574 0.6748

LTG 20687 0.1623 0.0682 0.1175 0.1500 0.1933

DISP 20687 0.1117 0.2516 0.0220 0.0438 0.0984

MVE 20687 3626.29 14632.54 203.96 616.54 1977.93

bmkt 20687 1.0996 0.5349 0.7604 1.0628 1.3958

bsmb 20687 0.6482 0.7814 0.1096 0.5654 1.0927

bhml 20687 0.0654 0.9221 -0.4717 0.1243 0.6650

BTD 20687 0.0155 0.0525 -0.0038 0.0174 0.0408

ABS_BTD 20687 0.0384 0.0390 0.0124 0.0270 0.0506

BTD_STD 20687 0.0412 0.0544 0.0144 0.0251 0.0459

EXP_BTD 12997 0.0246 0.0691 -0.0069 0.0239 0.0579

EXP_BTD_STD 12997 0.0442 0.0424 0.0211 0.0326 0.0516

IU 12997 -0.0096 0.0565 -0.0381 -0.0046 0.0243

ABS_IU 12997 0.0420 0.0400 0.0138 0.0305 0.0570

IU_STD 12997 0.0409 0.0279 0.0226 0.0339 0.0504

Ravg_rf is the implied cost of equity capital for firm i in June of year t minus the year t yield on a 10-year U.S. Treasury note. BM equals the book value of equity divided by the market value of equity, measured at the beginning of the year. LTG is the I/B/E/S analyst consensus long-term growth in earnings per share forecast reported in June of year t. If long-term growth forecast is not available, LTG equals the two-year-ahead earnings forecast divided by the one-year-ahead forecast minus one. DISP (dispersion) is the standard deviation of analyst estimates for year t earnings divided by the consensus forecast for year t earnings. MVE equals the market value of equity at the beginning of the year. βMKT, βSMB, and βHML are estimates from the Fama and French (1993) three-factor model to adjust for systematic risk. BTD is the level of book-tax differences. ABS_BTD is the absolute value of the level of book-tax differences. BTD_STD is the standard deviation of book-tax differences calculated over years t-4 through t. EXP_BTD is the predicted BTD from equation (2). EXP_BTD_STD is the standard deviation of EXP_BTD. IU, residuals from equation (2), is the information uncertainty proxy. ABS_IU is the absolute values of IU. IU_STD is the standard deviation of information uncertainty proxy calculated over years t-4 through t.

37

Ravg_rf lnBM LTG lnDISP lnMVE βmkt βsmb βhml HiBTD LoBTD ABS_BTD BTD_STD EXP_BTD EXP_BTD_STD IU ABS_IU IU_STD

Ravg_rf 0.308 0.098 0.314 -0.271 0.160 0.218 0.165 -0.038 0.118 0.042 0.136 -0.218 0.144 0.132 -0.020 0.106<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.023 <.0001

lnBM 0.342 -0.318 0.329 -0.440 0.061 0.143 0.190 -0.158 0.072 -0.128 -0.159 -0.294 -0.186 0.285 -0.229 -0.191<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

LTG 0.060 -0.318 0.068 -0.165 0.123 0.236 -0.260 0.079 0.041 0.152 0.258 -0.009 0.271 0.003 0.120 0.188<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.285 <.0001 0.729 <.0001 <.0001

lnDISP 0.274 0.356 0.023 -0.333 0.154 0.206 -0.068 -0.047 0.205 0.121 0.172 -0.279 0.190 0.182 -0.002 0.090<.0001 <.0001 0.001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.860 <.0001

lnMVE -0.271 -0.426 -0.194 -0.333 -0.017 -0.486 0.023 0.031 -0.078 -0.042 -0.087 0.158 -0.090 -0.137 0.004 -0.050<.0001 <.0001 <.0001 <.0001 0.012 <.0001 0.001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.641 <.0001

βmkt 0.185 0.080 0.134 0.166 -0.003 0.062 0.165 -0.007 0.079 0.056 0.167 -0.129 0.185 0.074 0.026 0.141<.0001 <.0001 <.0001 <.0001 0.623 <.0001 <.0001 0.310 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.003 <.0001

βsmb 0.237 0.162 0.246 0.209 -0.505 0.054 0.090 0.002 0.063 0.064 0.151 -0.122 0.174 0.100 0.012 0.099<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.766 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.186 <.0001

βhml 0.212 0.183 -0.261 -0.065 0.041 0.177 0.083 -0.038 -0.040 -0.105 -0.133 -0.084 -0.160 0.098 -0.118 -0.135<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

HiBTD -0.042 -0.156 0.079 -0.039 0.026 -0.011 -0.003 -0.033 -0.249 0.485 0.151 0.252 0.115 0.230 0.045 0.112<.0001 <.0001 <.0001 <.0001 0.000 0.109 0.661 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

LoBTD 0.107 0.081 0.019 0.187 -0.078 0.068 0.062 -0.035 -0.249 0.206 0.169 -0.320 0.119 -0.225 0.179 0.120<.0001 <.0001 0.006 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

ABS_BTD -0.028 -0.100 0.097 0.079 -0.028 0.011 0.027 -0.074 0.572 0.151 0.407 -0.248 0.320 0.003 0.243 0.261<.0001 <.0001 <.0001 <.0001 <.0001 0.120 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.775 <.0001 <.0001

BTD_STD 0.150 -0.104 0.178 0.199 -0.077 0.136 0.114 -0.083 0.217 0.246 0.351 -0.124 0.687 0.031 0.155 0.532<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.000 <.0001 <.0001

EXP_BTD -0.248 -0.365 0.073 -0.263 0.151 -0.124 -0.127 -0.120 0.271 -0.291 0.170 -0.093 -0.138 -0.532 0.164 -0.033<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.000

EXP_BTD_STD 0.153 -0.139 0.199 0.177 -0.075 0.132 0.117 -0.093 0.111 0.131 0.170 0.483 -0.075 1.000 0.033 0.229 0.651<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.000 <.0001 <.0001

IU 0.156 0.277 -0.014 0.202 -0.142 0.079 0.111 0.089 0.257 -0.222 0.135 0.081 -0.619 0.049 -0.394 -0.068<.0001 <.0001 0.097 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

ABS_IU -0.028 -0.174 0.116 -0.009 -0.006 0.009 0.018 -0.101 0.068 0.144 0.126 0.181 0.157 0.254 -0.204 0.3940.001 <.0001 <.0001 0.295 0.476 0.315 0.045 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

IU_STD 0.113 -0.172 0.162 0.061 -0.044 0.085 0.071 -0.085 0.118 0.127 0.160 0.504 -0.006 0.666 -0.029 0.353<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.497 <.0001 0.001 <.0001

Panel B: Pearson (Spearman) correlations above (below) the diagonal for equation variables

Ravg_rf is the implied cost of equity capital for firm i in June of year t minus the year t yield on a 10-year U.S. Treasury note. BM equals the book value of equity divided by the market value of equity, measured at the beginning of the year. LTG is the I/B/E/S analyst consensus long-term growth in earnings per share forecast reported in June of year t. If long-term growth forecast is not available, LTG equals the two-year-ahead earnings forecast divided by the one-year-ahead forecast minus one. lnDISP (dispersion) is the natural log of the standard deviation of analyst estimates for year t earnings divided by the consensus forecast for year t earnings. lnMVE equals the natural log of the market value of equity at the beginning of the year. βMKT, βSMB, and βHML are estimates from the Fama and French (1993) three-factor model to adjust for systematic risk. HiBTD is an indicator variable equals to one if an observation is in the highest quintile of BTD rank variables. LoBTD is an indicator variable equals to one if an observation is in the lowest quintile of BTD rank variables. ABS_BTD is the absolute value of the level of book-tax differences. BTD_STD is the standard deviation of book-tax differences calculated over years t-4 through t. EXP_BTD is the predicted BTD from equation (2). EXP_BTD_STD is the standard deviation of EXP_BTD. IU is the information uncertainty (residuals from equation (2)). ABS_IU is the absolute value of IU. IU_STD is the standard deviation of information uncertainty proxy calculated over years t-4 through t.

38

Table 4 Results of Testing Hypothesis 1

Ravg_rf_it = α0 + α 1 lnBMit + α 2 LTGit + α 3 lnDISPit + α 4 lnMVEit + α 5 βMKTit + α 6 βSMBit + α 7 βHMLit

+ α 8 HiBTDit + α9 LoBTDit + α 10 ABS_BTDit + α 11 BTD_STDit + Σα j IndustryDummiesit + Σα k YearDummiesit + εit

N = 20,687 Dependent Variable = Ravg_rf

Variablea

Pred Sign

(1) (2) (3) (4)

lnBM + 0.0116 0.0119 0.0119 0.0120 (7.91) *** (8.27) *** (8.16) *** (8.99) ***

LTG + 0.0644 0.0641 0.0628 0.0632 (6.93) *** (6.88) *** (6.60) *** (6.82) ***

lnDISP + 0.0069 0.0069 0.0068 0.0066 (13.35) *** (12.76) *** (13.40) *** (13.62) ***

lnMVE - -0.0022 -0.0021 -0.0021 -0.0020 (-3.74) *** (-3.71) *** (-3.60) *** (-3.61) ***

βMKT + 0.0017 0.0016 0.0013 0.0013

(1.98) ** (1.91) * (1.50) (1.66) *

βSMB + 0.0012 0.0011 0.0010 0.0010

(1.38) (1.31) (1.17) (1.17)

βHML + 0.0024 0.0024 0.0026 0.0026

(3.65) *** (3.75) *** (3.90) *** (4.34) ***

HiBTD + 0.0021 0.0003

(3.63) *** (0.36)

LoBTD + 0.0029 0.0017

(5.92) *** (2.68) ***

ABS_BTD + 0.0406 0.0244

(4.59) *** (1.99) **

BTD_STD + 0.0330 0.0246

(3.50) *** (2.85) ***

Adj. R2 0.2614 0.2624 0.2628 0.2645 ***, **, * indicates that the coefficient estimate is significant at 0.01, 0.05, and 0.1 in two-tailed tests. a Ravg_rf is the implied cost of equity capital for firm i in June of year t minus the year t yield on a 10-year U.S. Treasury note. BM equals book value of equity divided by market value of equity, measured at the beginning of the year. LTG is the I/B/E/S analyst consensus long-term growth in earnings per share forecast reported in June of year t. If long-term growth forecast is not available, LTG equals the two-year-ahead earnings forecast divided by the one-year-ahead forecast, minus one. lnDISP (dispersion) is the natural log of the standard deviation of analyst earnings forecasts for year t divided by the consensus forecast for year t. lnMVE equals the natural log of the market value of equity at the beginning of the year. βMKT, βSMB, and βHML are estimates from the Fama and French (1993) three-factor model to adjust for systematic risk. HiBTD, an indicator variable, equals to one if an observation is in the highest quintile of BTD rank variables. LoBTD, an indicator variable, equals to one if an observation is in the lowest quintile of BTD rank variables. ABS_BTD is the absolute value of the level of book-tax differences. BTD_STD is the standard deviation of BTDs calculated over years t-4 through t. IndustryDummies are based on Fama-French 48 industry classifications. YearDummies are based on years when cost of capital is estimated. Industry and year fixed effects are removed from all dependent and independent variables before estimating the regression with the two-dimensional clustering method. All t-statistics are computed using corrected standard errors with two-dimensional clustering by firm and year.

39

Table 5 Descriptive Statistics – BTD Model Variables

Panel A: Summary statistics

N Mean Std. Dev. Q1 Median Q3 BTD 75315 -0.0693 0.2879 -0.0420 0.0088 0.0359

SIZE 75315 4.3614 2.1516 2.8633 4.2479 5.7882 LEV 75315 0.1805 0.1924 0.0129 0.1313 0.2798 CAPINT 75315 0.3049 0.2235 0.1289 0.2522 0.4305 INVINT 75315 0.1773 0.1650 0.0231 0.1451 0.2846 RDINT 75315 0.1399 0.8988 0.0000 0.0000 0.0350 ROA 75315 -0.0001 0.2775 -0.0232 0.0605 0.1268 FORRATIO 75315 0.0539 0.2547 0.0000 0.0000 0.0000 DTAX 75315 -0.0047 0.1463 -0.0183 0.0026 0.0280 GROWTH 75315 0.2243 0.7763 -0.0322 0.0793 0.2366

Panel B: Pearson (Spearman) correlations above (below) the diagonal

BTD SIZE LEV CAPINT INVINT RDINT ROA FORRATIO DTAX GROWTH

BTD 0.310 0.007 0.075 0.089 -0.315 0.908 0.049 0.533 0.082

<.0001 0.041 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

SIZE 0.188 0.190 0.134 -0.097 -0.079 0.355 0.202 0.006 -0.001

<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.107 0.725

LEV 0.038 0.262 0.310 -0.059 -0.058 -0.053 -0.007 -0.020 -0.037

<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.036 <.0001 <.0001

CAPINT 0.128 0.162 0.364 -0.299 -0.108 0.045 -0.028 -0.019 -0.096

<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

INVINT 0.072 -0.057 0.024 -0.172 -0.112 0.100 -0.033 0.019 -0.103

<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

RDINT -0.137 -0.083 -0.248 -0.294 0.038 -0.333 -0.021 -0.157 0.060

<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

ROA 0.665 0.273 -0.119 0.035 0.135 -0.107 0.059 0.410 0.072

<.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001

FORRATIO 0.081 0.277 -0.001 -0.029 -0.016 0.114 0.137 0.013 -0.017

<.0001 <.0001 0.674 <.0001 <.0001 <.0001 <.0001 0.000 <.0001

DTAX 0.294 -0.073 -0.008 -0.042 -0.006 -0.010 0.102 0.011 0.155

<.0001 <.0001 0.019 <.0001 0.064 0.004 <.0001 0.001 <.0001

GROWTH 0.331 0.099 -0.005 -0.049 -0.029 -0.011 0.398 0.024 0.142

<.0001 <.0001 0.132 <.0001 <.0001 0.001 <.0001 <.0001 <.0001

BTD is the book-tax differences. SIZE is the log of total assets. LEV is the long-term debt divided by total assets. CAPINT is capital intensity (net PP&E divided by total assets) and INVINT is inventory intensity (inventory divided by total assets). RDINT is the R&D intensity (R&D expense divided by net sales). ROA is pre-tax income divided by total assets. FORRATIO is the ratio of foreign sourced pre-tax book income to total pre-tax book income. DTAX is the tax aggressive measures obtained based on Frank et al. (2009) method. GROWTH is the change in total assets divided by prior year total assets.

40

Table 6 Results of Equation (2)

BTDit = β0 + β1 SIZEit + β2 LEVit + β3 CAPINTit + β4 INVINTit + β5 RDINTit

+ β6 ROAit + β7 FORRATIOit + β8 DTAXit + β9 GROWTHit +εit.a

Dependent Variable = BTD

Variablea Coefficient

INTERCEPT -0.0711

(-26.04) ***

SIZE 0.0024

(6.97) ***

LEV 0.0409

(12.05) ***

CAPINT 0.0189

(5.39) ***

INVINT 0.0245

(2.86) ***

RDINT -0.1448

(-1.25)

ROA 0.6127

(63.59) ***

FORRATIO -0.0125

(-2.68) ***

DTAX 0.5156

(44.62) ***

GROWTH 0.0146

(6.69) ***

Adj. R2 0.7631

***, **, * indicates that the coefficient estimate is significant at 0.01, 0.05, and 0.1 in two-tailed tests. a Equation (2) is estimated for each of the Fama-French 48 industry groups in each year that have at least 15 firms. The tabled results are mean results of each industry-year regression. The total pooled sample of firms is 75,315. b BTD is current year book-tax difference. SIZE is the log of total assets. LEV is the long-term debt divided by total assets. CAPINT is capital intensity (net PP&E divided by total assets). INVINT is inventory intensity (inventory divided by total assets). RDINT is R&D intensity (R&D expense divided by net sales). ROA is pre-tax income divided by total assets. DTAX is the tax aggressive measures obtained based on Frank et al. (2009) method. GROWTH is the change in total assets divided by prior year total assets.

41

Table 7 Results of Testing Hypothesis 2

Ravg_rf_it = α0 + α 1 lnBMit + α 2 LTGit + α 3 lnDISPit + α 4 lnMVEit + α 5 βMKTit + α 6 βSMBit + α 7 βHMLit + α 8 EXP_BTDit

+ α 9EXP_BTD_STDit + α 10 ABS_IUit + α 11 IU_STDit + Σα j IndustryDummiesit + Σα k YearDummiesit + εit

(N = 12,997) Dependent Variable = Ravg_rf

Variablea

Pred Sign

(1) (2) (3)

lnBM + 0.0120 0.0124 0.0125

(7.82) *** (7.83) *** (7.93) ***

LTG + 0.0655 0.0642 0.0643

(8.31) *** (7.88) *** (7.88) ***

lnDISP + 0.0066 0.0064 0.0064

(14.00) *** (14.57) *** (14.52) ***

lnMVE - -0.0016 -0.0015 -0.0015 (-2.96) *** (-2.75) *** (-2.73) ***

βMKT + 0.0016 0.0012 0.0012 (2.40) ** (1.71) * (1.71) *

βSMB + 0.0012 0.0010 0.0010 (1.77) * (1.45) (1.46)

βHML + 0.0023 0.0026 0.0026 (4.49) *** (4.83) *** (4.80) ***

EXP_BTD ? -0.0008 0.0023 0.0019 (-0.13) (0.40) (0.30) EXP_BTD_STD ? 0.0303 0.0306 (2.06) ** (2.09) ** ABS_IU + 0.0146 0.0055 (2.08) ** (0.83) IU_STD + 0.0248 0.0218 (1.91) * (1.72) *

Adj. R2 0.2778 0.2807 0.2807 ***, **, * indicates that the coefficient estimate is significant at 0.01, 0.05, and 0.1 in two-tailed tests. a Ravg_rf is the implied cost of equity capital for firm i in June of year t minus the year t yield on a 10-year U.S. Treasury note. BM equals the book value of equity divided by the market value of equity, measured at the beginning of the year. LTG is the I/B/E/S analyst consensus long-term growth in earnings per share forecast reported in June of year t. If long-term growth forecast is not available, LTG equals the two-year-ahead earnings forecast divided by the one-year-ahead forecast minus one. DISP (dispersion) is the standard deviation of analyst estimates for year t earnings divided by the consensus forecast for year t earnings. MVE equals the market value of equity at the beginning of the year. βMKT, βSMB, and βHML are estimates from the Fama and French (1993) three-factor model to adjust for systematic risk. EXP_BTD is the predicted BTD from equation (2). EXP_BTD_STD is the standard deviation of EXP_BTD. ABS_IU is the absolute values of information uncertainty (residuals from equation (2)). IU_STD is the standard deviation of information uncertainty proxy calculated over years t-4 through t. IndustryDummies are based on Fama-French 48 industry classifications. YearDummies are based on years when the implied cost of capital is estimated. Industry and year fixed effects are removed from all dependent and independent variables before estimating the regression with the two-dimensional clustering method. All t-statistics are computed using corrected standard errors with two-dimensional clustering by firm and year.

42

Table 8 Sensitivity of Results

Ravg_rf_it = α0 + α1 lnBMit + α2 LTGit + α3 lnDISPit + α4 lnMVEit + α5 βMKTit + α6 βSMBit + α7 βHMLit + α8 AQit + α9 SMOOTHit + α10 abs_AAit + α11 PERSISit + α12 HIGHit + α13 HiBTDit + α14 HiBTD*HIGHit + α15 LoBTDit + α16 LoBTD*HIGHit + α17 ABS_BTDit + α18 ABS_BTD*HIGHit

+ α19 BTD_STDit + α20 BTD_STD*HIGHit + Σα j IndustryDummiesit + Σα k YearDummiesit + εit

Panel A: H1 (N = 16,398) Dependent Variable = Ravg_rf

Variablea Pred Sign (1) (2) (3) (4)

lnBM + 0.0122 0.0124 0.0123 0.0124

(8.41) *** (8.60) *** (8.57) *** (8.75) ***

LTG + 0.0627 0.0626 0.0613 0.0616

(5.98) *** (5.95) *** (5.76) *** (5.80) ***

lnDISP + 0.0063 0.0064 0.0063 0.0062

(12.12) *** (11.95) *** (12.15) *** (12.08) ***

lnMVE - -0.0019 -0.0019 -0.0019 -0.0019

(-3.58) *** (-3.51) *** (-3.47) *** (-3.51) ***

βMKT + 0.0011 0.0011 0.0011 0.0012

(1.41) (1.34) (1.38) (1.42)

βSMB + 0.0009 0.0009 0.0009 0.0009

(1.10) (1.07) (1.11) (1.10)

βHML + 0.0028 0.0028 0.0027 0.0027

(4.18) *** (4.24) *** (4.08) *** (4.10) ***

AQ + 0.0876 0.0851 0.0783 0.0780

(6.83) *** (6.40) *** (6.18) *** (6.18) ***

SMOOTH + 0.0025 0.0024 0.0023 0.0022

(3.66) *** (3.42) *** (3.78) *** (3.51) ***

abs_AA + 0.0111 0.0114 0.0118 0.0108

(3.41) *** (3.51) *** (3.75) *** (3.56) ***

PERSIS - -0.0008 -0.0008 -0.0007 -0.0008

(-1.99) ** (-1.91) * (-1.75) * (-2.00) **

HIGH ? 0.0011 0.0013 0.0023 0.0025

(1.71) * (1.67) * (3.31) *** (3.11) ***

HiBTD + 0.0018 0.0005

(1.75) * (0.42)

HiBTD*HIGH - -0.0005 0.0007

(-0.42) (0.57)

LoBTD + 0.0035 0.0024

(4.33) *** (2.44) **

LoBTD*HIGH - -0.0033 -0.0021

(-3.43) *** (-1.84) *

ABS_BTD + 0.0362 0.0117

(2.81) *** (0.81)

ABS_BTD*HIGH - -0.0260 0.0015

(-1.90) * (0.10)

BTD_STD + 0.0401 0.0334

(3.72) *** (2.97) ***

BTD_STD*HIGH - -0.0499 -0.0479

(-4.55) *** (-4.14) ***

Adj. R2 0.2927 0.2925 0.2940 0.2950

43

Notes to Table 8, Panel A

***, **, * indicates that the coefficient estimate is significant at 0.01, 0.05, and 0.1 in two-tailed tests. a Ravg_rf is the implied cost of equity capital for firm i in June of year t minus the year t yield on a 10-year U.S. Treasury note. BM equals book value of equity divided by market value of equity, measured at the beginning of the year. LTG is the I/B/E/S analyst consensus long-term growth in earnings per share forecast reported in June of year t. If long-term growth forecast is not available, LTG equals the two-year-ahead earnings forecast divided by the one-year-ahead forecast, minus one. lnDISP (dispersion) is the natural log of the standard deviation of analyst earnings forecasts for year t divided by the consensus forecast for year t. lnMVE equals the natural log of market value of equity at the beginning of the year. βMKT, βSMB, and βHML are estimates from the Fama and French (1993) three-factor model to adjust for systematic risk. AQ is accruals quality, the standard deviation of firm i’s residuals, from years t-4 to t from annual cross-sectional estimations of the modified Dechow and Dichev (2002) model. Smoothing is the standard deviation of income before extraordinary items divided by the standard deviation of cash flow from operations. ABS_AA is the absolute value of performance-adjusted abnormal accruals (McNichols 2000; Kothari et al., 2005). Persistence is the firm’s slope coefficient from an AR1 model of annual earnings. HiBTD, an indicator variable, equals to one if an observation is in the highest quintile of BTD rank variables. LoBTD, an indicator variable, equals to one if an observation is in the lowest quintile of BTD rank variables. ABS_BTD is the absolute value of the level of book-tax differences. BTD_STD is the standard deviation of BTDs calculated over years t-4 through t. HIGH is an indicator variable equals to one if an observation has institutional ownership percentage above median. IndustryDummies are based on Fama-French 48 industry classifications. YearDummies are based on years when cost of capital is estimated. Industry and year fixed effects are removed from all dependent and independent variables before estimating the regression with the two-dimensional clustering method. All t-statistics are computed using corrected standard errors with two-dimensional clustering by firm and year.

44

Table 8 (continued)

Ravg_rf_it = α0 + α1 lnBMit + α2 LTGit + α3 lnDISPit + α4 lnMVEit + α5 βMKTit + α6 βSMBit + α7 βHMLit + α8 AQit + α9 SMOOTHit + α10 abs_AAit + α11 PERSISit ++ α12 HIGHit + α13 EXP_BTDit + α14 EXP_BTD_STDit + α 15 ABS_IUit + α16 ABS_IU*HIGHit

+ α17 IU_STDit + α18 IU_STD*HIGHit + Σα j IndustryDummiesit + Σα k YearDummiesit + εit

Panel B: H2 (N = 11,149) Dependent Variable = Ravg_rf

Variablea Pred Sign (1) (2) (3)

lnBM + 0.0121 0.0124 0.0124

(7.67) *** (7.78) *** (7.77) ***

LTG + 0.0702 0.0695 0.0695

(7.49) *** (7.41) *** (7.44) ***

lnDISP + 0.0066 0.0064 0.0064

(12.51) *** (13.10) *** (13.08) ***

lnMVE - -0.0015 -0.0015 -0.0015 (-2.87) *** (-2.77) *** (-2.78) ***

βMKT + 0.0008 0.0008 0.0007 (0.99) (0.97) (0.91)

βSMB + 0.0010 0.0010 0.0010 (1.30) (1.23) (1.23)

βHML + 0.0031 0.0031 0.0031 (4.93) *** (4.88) *** (4.87) ***

AQ + 0.0708 0.0592 0.0569

(4.56) *** (3.99) *** (3.72) ***

SMOOTH + 0.0026 0.0019 0.0021

(3.80) *** (3.52) *** (3.54) ***

abs_AA + 0.0070 0.0045 0.0064

(1.64) (1.25) (1.64)

PERSIS - -0.0005 -0.0003 -0.0005

(-0.96) (-0.70) (-1.01)

HIGH ? 0.0011 0.0043 0.0044 (1.13) (3.70) *** (3.45) *** EXP_BTD ? 0.0072 0.0085 0.0086 (1.20) (1.49) (1.44) EXP_BTD_STD ? 0.0135 0.0144 (0.90) (0.96) ABS_IU + 0.0200 -0.0011 (1.93) * (-0.11)

ABS_IU*HIGH - -0.0313 -0.0008

(-2.09) ** (-0.05)

IU_STD + 0.0753 0.0772

(3.38) *** (3.54) ***

IU_STD*HIGH - -0.1108 -0.1123

(-4.94) *** (-4.80) ***

Adj. R2 0.2868 0.2905 0.2902

45

Notes to Table 8, Panel B ***, **, * indicates that the coefficient estimate is significant at 0.01, 0.05, and 0.1 in two-tailed tests. a Ravg_rf is the implied cost of equity capital for firm i in June of year t minus the year t yield on a 10-year U.S. Treasury note. BM equals book value of equity divided by market value of equity, measured at the beginning of the year. LTG is the I/B/E/S analyst consensus long-term growth in EPS forecast reported in June of year t. If long-term growth forecast is not available, LTG equals the two-year-ahead earnings forecast divided by the one-year-ahead forecast, minus one. lnDISP (dispersion) is the natural log of the standard deviation of analyst earnings forecasts for year t divided by the consensus forecast for year t. lnMVE equals the natural log of market value of equity at the beginning of the year. βMKT, βSMB, and βHML are estimates from the Fama and French (1993) three-factor model to adjust for systematic risk. AQ is accruals quality, the standard deviation of firm i’s residuals, from years t-4 to t from annual cross-sectional estimations of the modified Dechow and Dichev (2002) model. Smoothing is the standard deviation of income before extraordinary items divided by the standard deviation of cash flow from operations. ABS_AA is the absolute value of performance-adjusted abnormal accruals (McNichols 2000; Kothari et al., 2005). Persistence is the firm’s slope coefficient from an AR1 model of annual earnings. EXP_BTD is the predicted BTD from equation (2). EXP_BTD_STD is the standard deviation of EXP_BTD. ABS_IU is the absolute values of information uncertainty (residuals from equation (2)). IU_STD is the standard deviation of information uncertainty proxy calculated over years t-4 through t. HIGH is an indicator variable equals to one if an observation has institutional ownership percentage above median. IndustryDummies are based on Fama-French 48 industry classifications. YearDummies are based on years when the implied cost of capital is estimated. Industry and year fixed effects are removed from all dependent and independent variables before estimating the regression with the two-dimensional clustering method. All t-statistics are computed using corrected standard errors with two-dimensional clustering by firm and year.

46

Table 9 Simultaneous Estimation of the Cost of Equity and Growth Rate

(N = 675) Dependent Variable = R_es_rf

Variablea (1) (2) (3) (4) (5) (6) (7)

lnBM_Median -0.0592 -0.0544 -0.0547 -0.0527 -0.0402 -0.0375 -0.0341

(-5.27) *** (-5.70) *** (-4.77) *** (-5.01) *** (-4.18) *** (-5.50) *** (-4.12) ***

lnMVE_Median 0.0010 0.0030 0.0022 0.0035 0.0080 0.0082 0.0092

(0.18) (0.52) (0.39) (0.60) (1.64) (1.86) * (1.98) *

βMKT_Median -0.0060 -0.0042 -0.0072 -0.0081 -0.0165 -0.0184 -0.0186

(-0.79) (-0.49) (-0.77) (-0.88) (-1.91) * (-2.02) * (-2.02) *

βSMB_Median 0.0060 0.0094 0.0066 0.0071 0.0100 0.0084 0.0104

(0.44) (0.67) (0.51) (0.57) (0.84) (0.69) (0.87)

βHML_Median 0.0196 0.0191 0.0189 0.0197 0.0267 0.0259 0.0260

(2.44) ** (2.16) ** (2.22) ** (2.41) ** (3.03) *** (2.91) *** (3.01) ***

HiBTD_Median 0.0593 -0.0021

(2.02) * (-0.05)

LoBTD_Median 0.0907 0.0387

(2.53) ** (1.75) *

ABS_BTD_Median 0.3999 0.3593

(2.14) ** (1.72) *

BTD_STD_Median 0.5277 0.4559

(3.01) *** (2.93) ***

EXP_BTD_Median -0.0614 0.0372 0.0198

(-0.45) (0.35) (0.18)

EXP_BTD_STD_Median 0.0658 0.0782

(0.49) (0.58)

ABS_IU_Median 0.4395 0.3159

(2.20) ** (1.88) *

IU_STD_Median 0.6216 0.4548

(2.81) *** (2.35) **

Adj. R2 0.234 0.239 0.242 0.246 0.239 0.239 0.241 OLS t-statistics corrected with two dimensional clustering by portfolio and year. ***, **, * indicates that the coefficient estimate is significant at 0.01, 0.05, and 0.1 in two-tailed tests. a Res_rf_ is the cost of equity estimated by Easton and Sommers (2007) minus the yield on the 10-year U.S. Treasury note in each year. lnBM_Median, lnMVE_Median, βMKT_Median, βSMB_Median, βHML_Median, HiBTD_Median, LoBTD_Median, ABS_BTD_Median, and BTD_STD_Median, EXP_BTD_Median, EXP_BTD_STD_Median, ABS_IU_Median, and IU_STD_Median are the median values of each variable in each of the 675 portfolios.