Taxes, Leverage, and the Cost of Equity Capitalschwert.ssb.rochester.edu/heitzman/DHL_JAR06.pdf · Taxes, Leverage, and the Cost of Equity Capital ... capital structure decisions,

DOI: 10.1111/j.1475-679X.2006.00214.xJournal of Accounting Research

Vol. 44 No. 4 September 2006Printed in U.S.A.

Taxes, Leverage, and the Costof Equity Capital

D A N D H A L I W A L , ∗ S H A N E H E I T Z M A N , † O L I V E R Z H E N L I ‡

Received 25 February 2005; accepted 10 January 2006

ABSTRACT

We examine the associations among leverage, corporate and investor leveltaxes, and the firm’s implied cost of equity capital. Expanding on Modiglianiand Miller [1958, 1963], the cost of equity capital can be expressed as a func-tion of leverage and corporate and investor level taxes. Based on this expres-sion, we predict that the cost of equity is increasing in leverage, and thatcorporate taxes mitigate this leverage-related risk premium, while the per-sonal tax disadvantage of debt increases this premium. We empirically testthese predictions using implied cost of equity estimates and proxies for thefirm’s corporate tax rate and the personal tax disadvantage of debt. Our resultssuggest that the equity risk premium associated with leverage is decreasing inthe corporate tax benefit from debt. We find some evidence that the equityrisk premium from leverage is increasing in the personal tax penalty associatedwith debt.

1. Introduction

In this paper, we examine the effect of taxes and leverage on a firm’scost of equity capital. A long stream of literature has sought to understandhow the corporate and investor level tax consequences of debt affect firmvalue and the cost of capital. Modigliani and Miller [1958] demonstrate that

∗University of Arizona and University of Auckland; †University of Rochester; ‡University ofNotre Dame. We thank workshop participants at Purdue University, Northwestern University,Stanford University, and the University of Washington as well as George Foster, David Larcker,and an anonymous referee for helpful comments and suggestions. We thank John Graham forproviding the simulated tax rates used in this study and I/B/E/S for providing analyst forecastdata.

691

Copyright C©, University of Chicago on behalf of the Institute of Professional Accounting, 2006

692 D. DHALIWAL, S. HEITZMAN, AND O. Z. LI

in the absence of taxes and transaction costs, firm value and the weightedaverage cost of capital are independent of capital structure. Holding theaverage cost of capital constant, they show that the cost of equity contains afinancial risk premium that is positively related to the firm’s leverage. Withcorporate taxes, Modigliani and Miller [1963] establish that the tax benefitprovided by the interest expense deduction increases firm value and reducesthe equity risk premium from leverage. Miller [1977] introduces the effectof personal level taxes into the analysis. He argues that individual investorsdemand a higher pretax return on debt to compensate for the personal taxon interest income. In equilibrium, the investor level tax disadvantage ofdebt can completely offset the corporate tax benefit, making capital struc-ture irrelevant. DeAngelo and Masulis [1980] argue that there is still a nettax benefit to debt, but show that in the presence of nondebt tax shields,the firm may not realize the full benefit of the interest expense deduction.In equilibrium, each firm equates the expected tax benefit of an additionaldollar of debt with the expected tax cost to investors.

Numerous studies, including MacKie-Mason [1990], Dhaliwal, Trezevant,and Wang [1992], and Graham [1999], examine the effect of corporateand investor level taxes on firms’ financial leverage and incremental financ-ing decisions. In general, their findings suggest that firms’ capital structurechoices correlate with corporate and investor level taxes in a predicted man-ner. These studies presume that economic considerations drive managers’capital structure decisions, but do not provide direct evidence that the taximplications of debt financing are reflected in firm value or the cost of eq-uity capital. Fama and French [1998] investigate whether leverage increasesfirm value consistent with the existence of a tax benefit to debt, but findthe opposite effect and conclude that nontax explanations dominate. Theyalso argue, “In short, good estimates of how the tax treatment of dividendsand debt affects the cost of capital and firm value are a high priority forresearch. . .” (Fama and French [1998, p. 819]). In this paper, we use esti-mates of the ex ante expected return implied by accounting-based valuationmodels to investigate whether the tax consequences of debt affect the firm’scost of equity capital.

Recent developments in the literature on accounting-based valuationmodels have expanded the available options for estimating the firm’s exante cost of equity capital. These approaches utilize variations on the resid-ual income valuation model (Ohlson [1995]) to infer investors’ expectedreturn from stock price, dividends, book value of equity, and forecasted fu-ture earnings. Numerous recent studies exploit these implied cost of equitycapital estimates to address a broad range of questions in accounting andfinance.1 If tax consequences affect the price investors are willing to payfor a given security, then the discount rate implied by the relation between

1 See, for example, Ashbaugh-Skaife, Collins, and LaFond [2004], Botosan [1997], Botosanand Plumlee [2002], Hail and Leuz [2006], Francis et al. [2004], Dhaliwal et al. [2005].

TAXES AND LEVERAGE 693

market price and expected future earnings should capture any tax-relatedpremium demanded by equity investors.

Modigliani and Miller [1958, 1963] show that the cost of equity capitalcontains a risk premium that is increasing in leverage (i.e., the equity riskpremium from leverage). They further show that the equity risk premiumfrom leverage is a function of corporate level taxes. We expand this expres-sion to incorporate the effect of investor level taxes.2 Comparative staticsindicate that corporate level taxes reduce the firm’s equity risk premiumfrom leverage, consistent with the corporate tax benefit of debt accruingto equity holders. In contrast, the personal tax penalty associated with debtincreases this premium, which is consistent with equity investors demandinga higher return for a given amount of leverage as the relative cost of debtfinancing increases.

To empirically test these predictions, we regress the firm’s implied costof equity capital on leverage and the interactions between leverage and thefirm’s estimated marginal tax rate, and between leverage and the personaltax penalty associated with debt. We use the simulated marginal corporatetax rate before financing described in Graham, Lemmon, and Schallheim[1998] to estimate the firm’s tax benefit from debt. We use the top individualstatutory rate on ordinary income as our proxy for the investor level tax rateon debt income and a weighted-average of individual tax rates on dividendsand capital gains to proxy for the investor level tax rate on equity income.Based on the estimated investor level tax rates on debt and equity income,we construct a proxy for the personal tax penalty associated with debt thatis increasing in the extent to which the investor level tax on debt incomeexceeds the investor level tax on equity.

The empirical results generally support our predictions. First, the impliedcost of equity capital is increasing in leverage, consistent with Modigliani andMiller [1958]. Second, the equity risk premium from leverage is decreasingin the firm’s estimated marginal tax rate before financing. This result sug-gests that the tax benefit from debt reduces the cost of equity and increasesmarket value. Third, the personal tax penalty associated with debt increasesthe equity risk premium from leverage in a pooled regression, but not incross-sectional regressions. Overall, the results provide support for the hy-pothesis that the corporate tax benefit from debt reduces the equity riskpremium from leverage, while the effect of personal taxes on this leverage-related premium appears to be driven by temporal variation in statutory taxrates.

This paper is related to a long stream of literature that investigates the ef-fect of corporate and investor level taxes on equity value and the firm’s cost ofcapital. Much of this literature focuses on the effect of dividend taxation onthe cost of equity capital and firm value using ex post realized returns (e.g.,Dhaliwal, Li, and Trezevant [2003], Litzenberger and Ramaswamy [1979])

2 See Taggart [1991] for a similar expression.


or event studies surrounding changes in statutory tax rates (e.g., Ayers,Cloyd, and Robinson [2002], Lang and Shackelford [2000]).3 A closelyrelated paper by Dhaliwal et al. [2005] uses ex ante cost of equity estimatesimplied by accounting-based valuation models to test whether the effect ofdividend taxes is capitalized in expected returns. Similar to Dhaliwal et al.[2005], we motivate the paper with a basic valuation model that links taxeswith pretax required returns and test whether the empirical evidence isconsistent with the theoretical predictions of the model. However, Dhaliwalet al. [2005] focus on the cost of equity capital implications of investor leveltaxes associated with a firm’s payout policy decisions. In contrast, we focuson the cost of equity effects of corporate and investor level taxes associatedwith the firm’s financing decisions.

We contribute to the literature by using firms’ ex ante cost of equityimplied by accounting-based valuation models to address the longstandingquestion of whether the tax consequences of leverage affect firm value andthe cost of equity. Generally, our findings suggest that the tax implicationsof capital structure decisions affect the firm’s cost of equity in the predictedmanner. This triangulates with prior research that shows that the capitalstructure decision is related to the firm-specific magnitude of the corporatetax benefit of debt and the personal tax penalty associated with debt.

The remainder of the paper is organized as follows. Section 2 develops thetheory and hypotheses. Section 3 discusses the empirical methodology andvariable selection. Section 4 presents the empirical results and sensitivityanalyses. Section 5 summarizes and concludes.

2. Theory and Hypotheses Development

2.1 LEVERAGE, TAXES, AND THE COST OF EQUITY CAPITAL

The results in Modigliani and Miller [1958, 1963] can be expanded todemonstrate how leverage and corporate and investor level taxes affect thefirm’s cost of equity capital (e.g., Taggart [1991]). Consider two firms withidentical productive assets. The expected cash flows generated by these twofirms, X , are identical. Firm U is an all equity firm and firm L has some debtin its capital structure. Assume that the corporate tax rate is τ c , the personallevel tax rate on equity income is τ ps , and the personal level tax rate on debtincome is τ pb. The total after-tax cash flow to capital providers of the leveredfirm, C L, is

C L = (X − rBL)(1 − τc )(1 − τps) + rBL(1 − τpb), (1)where BL is the market value of debt in firm L’s capital structure and r isthe interest rate on the debt. The first term of equation (1) is the after-taxcash flow to equity holders and the second term is the after-tax cash flow todebt holders. Equation (1) can be rewritten as

3 For a recent review of the literature on the effect of taxes on asset prices, see Shackelfordand Shevlin [2001].


C L = X(1 − τc )(1 − τps) + r (1 − τpb)BL

[1 − (1 − τc )(1 − τps)

1 − τpb

]. (2)

The first term of equation (2) represents the after-tax cash flow to the all-equity firm U and the second term represents the cash flow benefit of debtafter considering both corporate and personal level taxes on equity and debt.If we capitalize the above cash flow stream using the appropriate after-taxdiscount rates on equity and debt income, we obtain the relation betweenthe value of the levered firm L, V L, and the value of the unlevered firm U ,V U ,

VL = VU +[

1 − (1 − τc )(1 − τps)1 − τpb

]BL. (3)

Thus, the value of the levered firm is equal to the value of an all-equityfirm plus the gain from leverage (Miller [1977]). The second term in equa-tion (3) represents the value of the capitalized debt tax shield after consid-ering personal tax rates on equity and debt income. Note that if τ pb = τ ps ,then we obtain V L = V U + τ cBL, as in Modigliani and Miller [1963]. Miller[1977] argues that if the tax rate on equity income is zero (i.e., τ ps = 0),then (1 − τ pb) = (1 − τ c) in equilibrium and the tax benefit from debtcompletely disappears. However, DeAngelo and Masulis [1980] argue thatτ pb < τ c + τ ps(1 − τ c) in equilibrium. Thus, there is still a net gain fromleverage, although less than the amount predicted by Modigliani and Miller[1963].

By definition, V L = S L + BL and V U = S U , where S L (S U ) is the marketvalue of equity for the levered (unlevered) firm. Substituting the expressionsV L and V U into equation (3), we obtain

SL + BL = SU +[

1 − (1 − τc )(1 − τps)1 − τ pb

]BL, (4)

which is equivalent to

SU = SL + (1 − τc )(1 − τps)1 − τpb

BL. (5)

We are interested in determining how the relation between the cost of eq-uity and leverage is affected by corporate and personal taxes. The valueof levered and unlevered equity can be expressed as a perpetual stream ofafter-corporate tax earnings capitalized at the appropriate rate to obtain

SU = X(1 − τc )KU

and (6)

SL = (X − rBL)(1 − τc )KL

, (6′)

where K U is the cost of unlevered equity and K L is the cost of levered equity.We set equations (6) and (6′) equal to X (1 − τ c) and combine to obtain


KL = SU

SLKU − r (1 − τc )

BL

SL. (7)

After substituting equation (5) into equation (7), we obtain

KL = KU + (1 − τc )[

KU1 − τps

1 − τpb− r

]BL

SL, (8)

where BL/S L is the debt-to-equity ratio of the firm. Equation (8) indicatesthat the cost of equity is a function of leverage and corporate and investorlevel taxes.

In the absence of taxes, equation (8) simplifies to

KL = KU + (KU − r )BL

SL, (9)

which is equivalent to the expression derived by Modigliani and Miller [1958,p. 272] for the cost of equity in the absence of taxes. That is, the expectedyield of a share of stock is equal to the appropriate capitalization rate K U

for a pure equity stream in the firm’s risk class, plus a premium related tofinancial risk that is equal to the product of the debt-to-equity ratio and thespread between the cost of capital for the all-equity firm and the cost of debt.

If corporate taxes are introduced, equation (8) becomes

KL = KU + (1 − τc )(KU − r )BL

SL, (10)

which is equivalent to the expression in Modigliani and Miller [1963, p. 439].Note that due to corporate level taxes the equity risk premium from leveragein equation (10), KU − r , is smaller by a factor of one minus the corporatetax rate. That is, the tax benefit from debt offsets the leverage-related riskpremium demanded by equity holders.

When investor level taxes are introduced, the value of the tax benefitfrom debt depends on the marginal investors’ relative tax rates on interestand equity income. If the tax rate on interest income is greater than thaton equity income, the value of the tax benefit from debt will be reduced,increasing the equity risk premium associated with leverage. The followingdiscussion utilizes equation (8) to derive our empirical predictions relatedto the effect of leverage and corporate and personal taxes on the cost ofequity capital.

We are interested in understanding how taxes affect the leverage-relatedrisk premium demanded by equity holders. We first take the derivative ofK L with respect to BL/S L in equation (8) to obtain

∂KL

∂(BL/SL)= (1 − τc )

[KU

1 − τps

1 − τpb− r

]. (11)

This represents the theoretical equity risk premium from leverage in ourmodel. Equation (11) is positive as long as K U (1 − τ ps) > r(1 − τ pb). That is,the effect of leverage on the cost of equity is positive as long as the after-taxreturn on equity is greater than the after-tax return on debt. This appears


reasonable over a relevant range of leverage, as suggested in Modigliani andMiller [1958]. Consistent with prior literature, the first hypothesis is:

H1: The firm’s cost of equity is increasing in leverage.

To examine the effect of corporate taxes on the equity risk premiumfrom leverage, we take the derivative of K L with respect to BL/S L and τ c inequation (8) to obtain

∂2 KL

∂(BL/SL)∂τc= −KU

1 − τps

1 − τpb+ r. (12)

Equation (12) is negative as long as K U (1 − τ ps) > r (1 − τ pb). That is,the effect of corporate taxes on the equity risk premium from leverage isnegative as long as the after-tax return on equity is greater than the after-taxreturn on debt. This implies that the effect of leverage on cost of equity isdecreasing in the corporate tax benefit provided by the interest expensededuction. Thus, our second hypothesis is:

H2: The effect of leverage on the firm’s cost of equity is decreasing inthe firm’s tax benefit from debt.

To investigate how personal level taxes affect the equity risk premiumfrom leverage, we use (1 − τ ps)/(1 − τ pb) to proxy for the personal taxdisadvantage of debt. Within the DeAngelo and Masulis [1980] framework,this ratio captures the relative pretax rates of return demanded by debt andequity investors. This term is increasing in the personal tax disadvantage ofinterest income and is multiplied by (1 − τ c) in equation (3) to determinethe net gain to leverage. We take the derivative of K L in equation (8) withrespect to BL/S L and (1 − τ ps)/(1 − τ pb) to obtain

∂2 KL

∂(BL/SL)∂[(1 − τps)/(1 − τpb)]= KU (1 − τc ) > 0. (13)

Equation (13) implies that the effect of leverage on the cost of levered equityis increasing in the personal tax disadvantage associated with debt. Theintuition behind this result can be argued within the theoretical contextof Miller [1977] and DeAngelo and Masulis [1980]. In theory, as the taxrate on interest income increases relative to the tax rate on equity income,bondholders demand higher relative pretax returns to leave them equallywell off on an after-tax basis. The resulting higher interest cost reduces thetax benefit from debt accruing to equity holders. As a result, the equity riskpremium from leverage should be increasing in the personal tax penalty oninterest income. Thus, the third hypothesis that we test is:

H3: The effect of leverage on the firm’s cost of equity is increasing inthe personal tax penalty associated with debt.

Empirical evidence consistent with these hypotheses provides support forthe view that the tax consequences of capital structure decisions are relevantto equity holders’ expected returns.


2.2 THE ROLE OF DIVIDEND POLICY

Miller and Modigliani [1961] demonstrate that in the absence of taxes,dividend policy does not affect firm value. However, they acknowledge thatdifferential taxation of dividends and capital gains can change this conclu-sion. Brennan [1970] shows that if the tax rate on dividends is higher thanthat on capital gains, the cost of equity capital should increase in dividendyield.4 Recent empirical evidence is consistent with this prediction (e.g.,Ayers, Cloyd, and Robinson [2002], Dhaliwal, Li, and Trezevant [2003],Dhaliwal et al. [2005]).

In a related paper, Dhaliwal et al. [2005, p. 5] follow Poterba and Summers[1985] and model the before-tax expected return on equity, R BT , as

RBT = RTF

1 − τcg+ τd − τcg

1 − τcgy , (14)

where R TF is the return on a tax-free security of equivalent risk and y is theexpected dividend payment divided by equity value. The focus of Dhaliwalet al. [2005] is whether dividend taxation affects expected returns, whereasour focus is whether the tax consequences of capital structure affect thecost of equity. However, the expressions for the expected return on equityin Dhaliwal et al. [2005] and in this paper must be identical for a givenamount of risk and leverage.

To show the relation between the two models, we first assume that equa-tion (14) holds within a risk class, where leverage is constant within thatclass. If leverage is set equal to zero, then it must be that

R(B/S)=0BT = R(B/S)=0

TF

1 − τcg+ τd − τcg

1 − τcgy

= KUZ + τd − τcg

1 − τcgy = KU . (15)

We interpret K UZ as the cost of capital for an all-equity firm that pays nodividends. After substituting equation (15) for K U in equation (8), we obtain

KL = KUZ + τd − τcg

1 − τcgy + (1 − τc )

[(KU Z + τd − τcg

1 − τcgy)

1 − τps

1 − τpb− r

]BL

SL.

(16)

This expression implies that the dividend policy of the firm has two po-tential effects: first, it increases the cost of equity when dividends are taxdisadvantaged independent of leverage, and second, it affects the equityrisk premium from leverage via both τ ps , the weighted-average tax rate on

4 The presence of dividend tax clienteles can mitigate this dividend tax effect (Litzenbergerand Ramaswamy [1979, 1980, 1982]).


equity income, and K U , the cost of capital for the all-equity firm.5 In otherwords, the tax treatment of dividends at the investor level is presumed toaffect expected returns independent of leverage, but is also correlated withthe personal tax penalty associated with debt. Therefore, we incorporatethe effect of dividend taxation into the empirical model.

3. Empirical Methodology

In this section, we empirically examine the effect of corporate and in-vestor level taxes on the association between a firm’s leverage and its cost ofequity capital. To operationalize tests of the theoretical predictions derivedin equations (11) to (13), we require estimates of the firm’s cost of equity,leverage, and corporate tax rate, and the marginal investors’ tax rates onequity and debt income. We begin this section with a description of ourestimate of the cost of equity, and continue with a discussion of the variouscorporate and personal level tax rates used in this study.

3.1 IMPLIED COST OF EQUITY CAPITAL

We use the discount rate implied from variations on the residual incomevaluation model to estimate the firm’s cost of equity, K L. This estimationapproach utilizes theoretical relationships between observed market valuesand forecasted earnings, dividends, and book values of equity to infer thepretax return required by the price-setting shareholder. At a theoreticallevel, ex ante estimation is more appropriate for estimating the return de-manded by shareholders than methods that rely on ex post realizations.

Several recent studies have used one or more implied cost of equitymeasures to examine various questions in accounting and finance (e.g.,Botosan and Plumlee [2002], Francis et al. [2004], Hail and Leuz [2006]).We estimate the cost of equity for our sample firms using the methodologiesdescribed in Gebhardt, Lee, and Swaminathan [2001], Claus and Thomas[2001], Gode and Mohanram [2003], and Easton [2004]. We refer to theseestimates as r gls , r ct , rojn,, and r mpeg , respectively. All four of these measureshave been used in the literature to estimate the firm’s cost of equity; how-ever, there is considerable variation in the magnitude of the associationsbetween the various implied cost of equity estimates and individual riskproxies, and there does not appear to be a consensus as to the superiority ofany particular model in estimating the cost of equity. For example, Botosanand Plumlee [2005] find that r gls is not consistently related to risk proxies,while Guay, Kothari, and Shu [2005] find that r gls is the best predictor offuture realized returns. Limiting empirical analysis to just one measure mayproduce spurious results if particular attributes of the model are correlated

5 It can be shown that when dividends are zero (i.e., y = 0) or when the tax rates on dividendsand capital gains are equal, the equity risk premium from leverage is not a function of thedividend tax rate.


with the variable of interest. To mitigate the effect that particular assump-tions of each model might have on our results, we follow Hail and Leuz[2006] and use the average of the four implied cost of equity estimates inour empirical tests. We also present results for the individual cost of equityestimates to show how the associations among leverage, taxes, and the costof equity vary across the models.

The appendix describes in detail the four models used to estimate thefirm’s cost of equity, the input variable definitions, and particular definitionsor assumptions unique to each model. We follow Gebhardt, Lee, and Swami-nathan [2001] and Gode and Mohanram [2003] and calculate the cost ofequity at the end of June for each year t. For all measures, we require thatthe firm have one- and two-year-ahead earnings-per-share forecasts (FEPS t +1and FEPS t +2) and either a three-year-ahead earnings forecast (FEPS t +3) orlong-term growth forecast (LTG). The Gode and Mohanram [2003] appli-cation requires that FEPS t +1 ≥ 0 and FEPS t +2 ≥ 0, while Easton [2004] addsthe condition that FEPS t +2 ≥ FEPS t +1 > 0. We require sample firms to haveall four measures in order to calculate the average equity risk premium, r avg .When using r gls , r ct , rojn,, or r mpeg as the dependent variable, we utilize allavailable observations.

Cost of equity estimates are obtained by searching over the range of 0%to 100% for the value that minimizes the difference between the discountedfuture earnings and the current market price. The exception is r ojn, whichcan be estimated explicitly. The primary cost of equity proxy used in our em-pirical tests, r avg , is the average of the four implied cost of equity estimates.To obtain the equity risk premiums used in the empirical tests, we subtractthe yield on a 10-year Treasury note. Annual risk premium estimates derivedfrom the four models, and the sample average across the four measures, arereported in panel A of table 1. The magnitudes of the premiums are gen-erally consistent with those obtained in prior studies. The mean (median)risk premium over the sample period is 4.95% (4.30%). Consistent withprior research, r mpeg and r ojn produce the largest equity risk premium esti-mates, whereas r gls produces the smallest (e.g., Botosan and Plumlee [2005],Guay, Kothari, and Shu [2005]). Spearman correlation coefficients betweenthe individual risk premiums and the average measure are shown in panelB and reveal the expected positive correlations between these measures,with the highest correlation between r mpeg and r ojn. The correlation coeffici-ents between r avg and the individual measures range from 0.676 to 0.916.

3.2 CORPORATE AND PERSONAL TAX RATES

Equation (11) predicts that the effect of leverage on the cost of equityis a function of the firm’s tax rate, τ c . If the firm expects to have positivetaxable income in current and future years, τ c is generally equal to thetop marginal corporate tax rate. If the firm cannot fully utilize its interestdeductions in the period paid, τ c should depend on the tax attributes ofthe firm, including the effect of net operating loss (NOL) carryforwards,investment tax credits (ITC), and the alternative minimum tax (AMT).


T A B L E 1Descriptive Data and Correlation Coefficients for Implied Cost of Equity Premiums

This table presents annual sample means of equity risk premium estimates. r gls , r ct , r ojn , andr mpeg are the implied cost of equity estimates derived from the models described in the appendixless the rate on a 10-year Treasury note. r avg is the average of r gls , r ct , r ojn , and r mpeg for firmswith cost of capital estimates available from all four models. Correlation coefficients are averageannual Spearman correlations.

All correlation coefficients are significant at the 0.001 level.

Panel A: Annual average of cost of equity premiumsYear N (r avg ) r avg r gls r ct r ojn r mpeg

1982 719 5.09 1.97 5.53 6.81 6.371983 820 4.22 1.82 3.59 6.60 5.891984 913 3.85 0.95 4.69 5.67 4.651985 883 4.43 2.33 4.56 5.97 5.301986 865 4.59 3.09 5.11 6.03 5.881987 866 4.13 2.24 4.28 5.66 5.561988 807 4.08 2.89 4.74 5.20 6.761989 803 4.19 3.21 5.04 5.19 4.631990 829 4.48 2.62 4.66 5.66 5.521991 848 4.58 2.95 4.71 6.03 6.111992 885 5.40 3.51 4.94 6.80 7.221993 907 5.67 4.37 5.38 6.83 7.261994 973 4.80 3.60 5.05 5.96 5.901995 1,030 5.47 4.13 5.61 6.51 6.601996 997 4.38 3.12 4.57 5.51 5.411997 1,187 4.80 3.88 5.38 5.77 5.771998 1,273 5.62 5.27 6.64 6.65 6.791999 1,135 5.50 5.21 6.69 6.37 6.562000 994 5.99 5.60 7.45 6.71 6.892001 753 5.46 6.12 7.06 6.23 6.692002 731 5.63 6.32 6.74 6.60 7.392003 514 5.68 7.52 6.35 7.08 8.052004 588 5.02 6.10 4.73 5.66 6.04

N 20,320 22,873 22,769 20,537 20,377Mean 4.95 3.87 5.43 6.14 6.11

Median 4.30 2.71 3.69 5.49 4.98

Panel B: Spearman correlation coefficients between cost of equity estimatesr gls r ct r ojn r mpeg r avg

r gls 1.000 0.464 0.451 0.470 0.689r ct 1.000 0.493 0.415 0.676r ojn 1.000 0.942 0.916r mpeg 1.000 0.899r avg 1.000

An important issue is how to measure the tax benefit from debt capturedby τ c in equation (8). In theory, the level of debt should be increasing in themarginal tax rate of the firm. Most proxies for the firm’s marginal tax rateare based on earnings after interest costs are deducted.6 However, firms that

6 See Graham [1996b], Plesko [2003], and Shevlin [1990] for discussions and analyses ofvarious marginal tax rate proxies.


borrow more are more likely to exhaust taxable income and reduce theirmarginal tax rate; thus, the empirical association between leverage and themarginal tax rate after financing is likely to be negative. To address thismethodological issue, Graham, Lemmon, and Schallheim [1998] developa simulated marginal tax rate based on taxable income before financingcosts are considered. This tax rate approximates the potential tax benefit ofdebt as if the firm had no debt. Consistent with their prediction, they findthat leverage is positively (negatively) related to the simulated marginaltax rate before (after) financing. Because the before financing estimate ismore likely to capture the tax benefit from the firm’s existing debt, we usesimulated marginal tax rates before financing in the empirical tests anddiscuss results using alternative proxies in the sensitivity analyses. Annualmeans of the simulated marginal corporate tax rate before financing arepresented in table 2. For comparative purposes, we also present the annualmeans for simulated marginal tax rates after financing.7 Average simulatedmarginal tax rates are higher in the early period of the sample, consistentwith the higher statutory corporate tax rates in effect at that time.

τ pb represents the tax rate faced by the marginal investor in the firm’sdebt securities. Because identification of the marginal investor is generallynot possible, the researcher usually assumes the tax status of the marginalinvestor or infers their marginal tax rate from existing data when available.As an example of the latter, Poterba [1989] estimates the marginal investor’stax rate on interest income as (R taxable − Rtax−free)/R taxable , where R taxable is theyield on one-year Treasury issues that are taxable, and Rtax−free is the yield onone-year prime grade tax-exempt municipal bonds. The primary advantageof this measure is that it uses pretax yields on differentially taxed assets ofequivalent risk to back out the implicit tax rate on interest income for themarginal investor. The marginal tax rate on interest computed from thismeasure remains relatively stable from 1982 through 2000. Beginning in2001, the marginal tax rate estimate drops significantly and becomes morevolatile, which suggests that this method is likely to measure marginal taxrates with significant error in the recent period of our sample.8 To mitigatepotential problems caused by using the implicit tax rate approach, we assumethat the marginal investor in corporate debt is a fully taxable individual andset τ pb equal to the top marginal tax rate on ordinary income.9 Annualvalues of τ pb are presented in table 2.

τ ps represents the tax rate of the marginal investor in the firm’s equity.Unlike income derived from debt investments, income derived from equity

7 John Graham’s simulated tax rates are available at http://faculty.fuqua.duke.edu/∼jgraham/.

8 For the years 1996 through 2000, the mean implicit tax rate using monthly yield data is34.1% with a standard deviation of 2.5%. For the years 2001 through 2004, the mean implicittax rate is 17.1% with a standard deviation of 9.2%.

9 We investigate the sensitivity of our results to the tax rate implied by the yields on Treasuryand municipal securities in a later section.


T A B L E 2Summary Statistics for Personal and Corporate Tax Rate Variables

This table presents the annual values of economy-wide and firm-specific tax rate variables anddividend payout ratios used in this study for firms with nonmissing values of r avg . There are20,320 firm-year observations over the period 1982 through 2004. Year references the calendaryear in which the implied cost of equity estimate is made. d is equal to the dividends paid in themost recent fiscal year divided by average earnings before extraordinary items over the priorthree years. τ pb is the highest statutory tax rate on interest income. τ d is the highest statutorytax rate on dividend income, which equals τ pb for years 1982 through 2002 and 0.15 thereafter.τ cg is the highest statutory tax rate on capital gains income. τ ps is the average tax rate on equityincome and is equal to d·τ d + [1 − d]·α·τ cg ,, where α = 0.25. τ c is equal to the simulatedmarginal corporate tax rate.

τ c

(1 − τ ps)/ Before AfterYear d τ pb τ d τ cg τ ps (1 − τ pb) Financing Financing1982 0.331 0.500 0.500 0.200 0.198 1.602 0.455 0.4021983 0.331 0.500 0.500 0.200 0.199 1.602 0.448 0.3761984 0.322 0.500 0.500 0.200 0.195 1.610 0.447 0.3651985 0.326 0.500 0.500 0.200 0.197 1.606 0.447 0.3771986 0.312 0.500 0.500 0.200 0.190 1.619 0.444 0.3611987 0.295 0.390 0.390 0.280 0.165 1.369 0.444 0.3511988 0.288 0.280 0.280 0.280 0.131 1.208 0.383 0.3011989 0.278 0.280 0.280 0.280 0.128 1.211 0.334 0.2781990 0.284 0.280 0.280 0.280 0.130 1.209 0.331 0.2741991 0.281 0.310 0.310 0.280 0.137 1.250 0.332 0.2711992 0.295 0.310 0.310 0.280 0.141 1.245 0.333 0.2671993 0.289 0.396 0.396 0.280 0.164 1.383 0.327 0.2521994 0.275 0.396 0.396 0.280 0.160 1.391 0.325 0.2591995 0.242 0.396 0.396 0.280 0.149 1.409 0.331 0.2661996 0.234 0.396 0.396 0.280 0.146 1.413 0.335 0.2651997 0.183 0.396 0.396 0.200 0.113 1.468 0.325 0.2611998 0.175 0.396 0.396 0.200 0.110 1.473 0.316 0.2611999 0.186 0.396 0.396 0.200 0.115 1.466 0.325 0.2472000 0.180 0.396 0.396 0.200 0.112 1.469 0.321 0.2532001 0.185 0.386 0.386 0.200 0.112 1.446 0.333 0.2442002 0.173 0.386 0.386 0.200 0.108 1.452 0.321 0.2272003 0.179 0.350 0.150 0.150 0.058 1.450 0.314 0.2512004 0.176 0.350 0.150 0.150 0.057 1.450 0.305 0.237

1982–2004 0.252 0.392 0.373 0.232 0.141 1.428 0.358 0.288

investments can be taxed at differential rates depending on the charac-ter of the income. Prior to 2003, dividend income earned by individualswas generally taxed at ordinary rates, while long-term capital gains incomehas generally been subject to preferential tax treatment. Therefore, τ ps inequation (8) represents a weighted-average tax rate on dividend and capitalgains income. We assume that the marginal investor is a taxable individualand that the applicable tax rates for this investor are capitalized into eq-uity prices; thus, payout policy becomes an important determinant of τ ps .Gordon and MacKie-Mason [1990] estimate τ ps as [d + (1 − d)·g ·α]·τ pb,where d is the amount per after-corporate tax dollar of earnings that isdistributed to shareholders in the form of a dividend, τ pb is the personal


tax rate on interest income, g represents one minus the exclusion ratio forlong-term capital gains income, and α is the benefit from deferring capitalgains. Note that d can be defined as either the firm-specific dividend pay-out ratio or an economy-wide ratio. Graham [1999] uses the firm-specificestimate of d to calculate τ ps and suggests that this specification is superiorto using an economy-wide estimate of payout policy.

We modify the equity tax rate equation from Gordon and MacKie-Mason[1990] to take into account specific tax rates on dividend income createdby the Jobs and Growth Tax Relief Reconciliation Act of 2003 (JGTRRA2003) and the statutory tax rate on long-term capital gains income. In ourstudy, τ ps = d·τ d + (1 − d)·α·τ cg , where τ d is the marginal rate on dividendincome, set equal to τ pb for years prior to 2003, and 0.15 thereafter, τ cg isset equal to the top statutory tax rate on long-term capital gains income,and α is the benefit of capital gains deferral. Following Graham [1999], weassume that α = 0.25. We define d as the dividends paid for the most recentyear divided by the average earnings over the prior three years and winsorizethe value at zero and one. Average annual values of τ d , τ cg , τ ps , and d arepresented in table 2. Average dividend payout ratios decrease steadily overtime, from 0.331 in 1982 to 0.176 in 2004, a trend that likely reflects theoverall drop in the number of firms that pay dividends during our sampleperiod (Fama and French [2001]). Eighty-eight percent of our sample firmspaid dividends in 1982, compared with 44.2% in 2004.

The personal tax penalty associated with debt represents the relative taxdisadvantage of receiving a dollar of interest income versus a dollar of equityincome for individual investors. Larger values of the personal tax penaltyimply that equity financing is more attractive, as potential stockholders willrequire a lower pretax return relative to potential lenders. In our study, thepersonal tax penalty associated with debt is equal to (1 − τ ps)/(1 − τ pb),where τ pb is based upon statutory tax rates on ordinary income. To measure(1 − τ ps)/(1 − τ pb), we assume that the marginal investor in debt andequity securities is a taxable individual. To the extent this does not hold, thepersonal tax penalty of debt income is measured with error, and its effect inthe empirical tests will be attenuated.

Annual averages of (1 − τ ps)/(1 − τ pb) are presented in table 2. Thepenalty is relatively large in the first five years of the sample, and then dropsto its lowest value beginning in 1988, when the top personal statutory taxrates on ordinary and long-term capital gains income were both equal to28%. Beginning in 1993, the top personal tax rate on ordinary incomeincreased to 39.6%, and in 1997, the maximum long-term capital gains ratewas reduced to 20%. The overall effect was a shock to the personal taxdisadvantage of debt in 1993 and again in 1997.

3.3 EMPIRICAL MODEL

Equation (8) predicts that the cost of equity for the levered firm is afunction of the cost of capital for an all-equity firm plus an adjustment forthe effects of leverage. Direct empirical estimation of this nonlinear equa-tion is not straightforward, and given the assumptions used to derive the


expression, it is not clear whether it is appropriate.10 Rather, we extractthe fundamental relations between the variables of interest and test our hy-potheses using a linear specification.11 We estimate the following empiricalmodel using pooled and annual cross-sectional regressions:

ravg = θ0 + θ1 B/A + θ2τc + θ3(B/A) · τc + θ4(1 − τps)/(1 − τpb)

+ θ5(B/A) · (1 − τps)/(1 − τpb) + θ6Yield + θ7(τd − τcg )/(1 − τcg )

+ θ8Yield · (τd − τcg )/(1 − τcg ) + θ8βMKT + θ9βSMB + θ10βHML

+ θ11 ln(Dispersion) + θ12LTG + θk∈[13,24]Industryk + ε, (17)

where r avg is equal to the average implied cost of equity premium estimatedusing the four methods described in the appendix in June of year t. We cal-culate r avg only for observations with nonmissing values of r gls , r ct , r ojn, andr mpeg . B/A is long-term debt divided by the market value of assets (total assetsless book value of stockholders equity plus the market value of equity) at theend of year t − 1.12 We predict a positive coefficient on B/A, consistent withempirical findings in Botosan and Plumlee [2005] and the general proposi-tion that leverage increases the financial risk of equity investors (Modiglianiand Miller [1958]).

τ c is defined as the simulated marginal tax rate before financing, andproxies for the estimated value of the tax benefit of debt. The coefficienton (B/A)·τ c tests whether the association between leverage and the costof equity is a function of the firm’s corporate tax rate, holding personaltaxes constant. H2 states that the effect of leverage on the cost of equity isdecreasing in the corporate tax rate; thus, we predict a negative coefficienton (B/A)·τ c . (1 − τ ps)/(1 − τ pb) is the personal tax penalty associated withdebt. The coefficient on (B/A)·(1 − τ ps)/(1 − τ pb) tests whether this penaltyaffects the association between leverage and the cost of equity. Consistentwith H3, we predict a positive sign for the coefficient on (B/A)·(1 − τ ps)/(1 − τ pb).

3.4 CONTROL VARIABLES

Using implied cost of equity estimates similar to those in this study,Dhaliwal et al. [2005] provide evidence that dividend taxes are capitalizedinto stock prices. To control for the effect of dividend policy on the firm’scost of equity, we include Yield, which is defined as the last annualized quar-terly dividend paid in year t–1 divided by the stock price at the beginningof the month. Dhaliwal et al. [2005] predict and find that the effect of Yieldon the implied cost of equity is increasing in the extent to which dividendsare tax disadvantaged. Similar to that study, we define the tax disadvantage

10 For example, dropping the assumption about the perpetuity of earnings and zerobankruptcy costs is likely to make the equation significantly more complex, though the essenceof its empirical implications should remain unchanged.

11 See Bowman [1980] and Dhaliwal [1986] for similar methodologies.12 In sensitivity tests, we explore alternative measures of leverage.


of dividends as (τ d − τ cg )/(1 − τ cg ), and interact it with Yield in the em-pirical model. Consistent with Dhaliwal et al. [2005], we predict a positivecoefficient on the interaction between Yield and (τ d − τ cg )/(1 − τ cg ).

We control for risk by including the Fama and French [1993] risk factorsβMKT , β SMB , and βHML in the model. We obtain these factors for firms withat least 24 months of stock return data ending in June of year t, and esti-mate the regression using up to 60 months of returns. These risk factorsare used to control for the effects of systematic risk, size, and the book-to-market ratio, which have been shown to be related to expected returns. Wealso include two controls for properties of analyst forecasts. Gebhardt, Lee,and Swaminathan [2001] and Gode and Mohanram [2003] find that an-alyst forecast properties explain cross-sectional variation in implied equityrisk premiums. ln(Dispersion) is the natural logarithm of the coefficient ofvariation in year t earnings forecasts issued in June of year t. LTG is themean long-term growth estimate reported in June of year t. Because we ex-pect analyst dispersion and expected growth to be positively correlated withrisk, we predict a positive coefficient on these variables. Industry controlsare based on the 12 industry classifications defined by Fama and French andare included to control for industry risk differences independent of capitalstructure.13

4. Empirical Results

4.1 DATA AND SAMPLE

To estimate the implied cost of equity estimates detailed in the appendix,we use analyst earnings estimates from the I/B/E/S Summary file and bookvalue and dividend data from Compustat. We obtain 29,963 firm-year obser-vations with at least one available cost of equity estimate from the modelsdescribed in the appendix and associated financial statement data. We elim-inate 2,295 observations with insufficient stock return data in CRSP to cal-culate risk proxies and an additional 4,794 observations in which simulatedtax rates are not available.

Our final sample of 22,874 firm-year observations covers the years 1982through 2004 and spans five major tax regimes. Table 3 contains descriptivedata and correlations between selected variables for the 20,320 observationswith a nonmissing value of r avg .14 r avg is measured in June of year t and fi-nancial statement information is measured as of the most recent fiscal yearending prior to April of year t. r avg is significantly correlated with the primary

13 These classifications are available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.

14 Because of our sample selection criteria, we tend to exclude small firms, firms that are notprofitable, and firms with little or no analyst coverage. Our sample represents approximately20% of the firm-year observations in Compustat, but about 60% of the market value. Themedian market value for Compustat firms is $68 million, compared with $469 million for oursample. The median ROA for Compustat firms is 2.69%, compared with 5.14% for our sample.


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variables in the expected direction. We also note the correlations betweenthe simulated marginal tax rates and leverage. τ c measured after financingis negatively related to B/A (coefficient = −0.093, p-value < 0.001), whileτ c measured before financing is positively related to B/A (coefficient =0.046, p-value < 0.001). The signs of these correlations are consistent withthe findings in Graham, Lemmon, and Schallheim [1998] and suggest thatinferences using marginal tax rate estimates based on earnings after financ-ing may be incorrect.

4.2 RESULTS

Results from estimating the empirical model using a pooled time-seriescross-sectional specification are presented in table 4. In column (1), wereport the results for a baseline regression excluding tax variables. Asexpected, the coefficient on B/A is positive and highly significant, consis-tent with Modigliani and Miller’s [1958] result. The remaining control vari-ables are generally significant and qualitatively similar to the results of priorliterature. Column (2) presents the results from interacting τ c with B/A.Consistent with H2, the coefficient on the interaction term is negative andsignificant (coefficient = −12.98, t-statistic = −8.15). This evidence suggeststhat the tax benefit of corporate debt reduces the equity risk premium asso-ciated with leverage. We next investigate whether the personal tax penaltyassociated with debt increases this leverage-related risk premium. In col-umn (3), we add (1 − τ ps)/(1 − τ pb) and the interaction between B/A and(1 − τ ps)/(1 − τ pb) to the model. Consistent with H3, the coefficient on theinteraction is positive and significant (coefficient = 5.18, t-statistic = 8.06).This suggests that higher tax rates on debt income relative to equity incomeincrease the relative cost of financing with debt, with the effect on cash flowspriced by equity holders.

In column (4) we introduce the effect of dividend yield and the dividendtax penalty into the model. Dhaliwal et al. [2005] find that the coefficienton Yield depends on the cost of equity estimate used, but that the coefficienton the interaction between Yield and (τ d − τ cg )/(1 − τ cg ) is consistentlypositive. We find similar evidence of dividend tax capitalization in our sam-ple. Specifically, the coefficient on the interaction between Yield and (τ d −τ cg )/(1 − τ cg ) is positive and significant (coefficient = 88.28, t-statistic =13.37). We also note that the coefficient on the interaction between B/Aand (1 − τ ps)/(1 − τ pb) drops to 3.38 (t-statistic = 5.10) when we control fordividend yield and the dividend tax penalty. This addresses the concern thatthe results for the personal tax penalty associated with debt may be drivenby dividend tax penalty effects documented in studies such as Dhaliwal et al.[2005], and supports the need to control for the effects of payout policy inthe empirical analysis. In column (5) we include industry effects. The coef-ficient on (B/A)·τ c falls in magnitude to −8.69 (t-statistic = −5.80), whichsuggests that marginal corporate tax rates may be correlated with some un-observed industry effects related to the association between leverage andthe cost of equity.


T A B L E 4Regression of Average Implied Equity Premiums on Leverage and Personal and Corporate Tax Variables

This table presents regression results from estimating a pooled time-series cross-sectional re-gression containing 20,320 observations over 1982 through 2004. The dependent variable isr avg , which equals the average of r gls , r ct , r ojn , and r mpeg for observations with all four estimatesavailable. B/A is the market value of debt divided by market value of assets at the end of yeart–1. τ c equals the simulated marginal tax rate before financing for year t–1. (1 − τ ps)/(1 − τ pb)is the personal tax penalty associated with debt. Yield is equal to the last annualized quarterlydividend paid in year t–1 divided by the stock price at the beginning of the month. (τ d −τ cg )/(1 − τ cg ) is the dividend tax penalty. βMKT , β SMB , and βHML are the Fama and Frenchrisk factors estimated using at least 24 and up to 60 monthly returns ending in June of yeart. Dispersion equals the standard deviation of analyst estimates for year t earnings divided bythe consensus forecast for year t earnings. LTG equals the mean long-term growth forecastavailable in June of year t. t-statistics are reported in parentheses.

Dependent Variable = r avg

Variable Name (1) (2) (3) (4) (5)B/A + 5.19 9.95 2.94 6.00 5.31

(34.23) (16.92) (2.81) (5.59) (5.11)τ c ? −6.08 −6.15 −6.04 −6.38

(−18.02) (−17.99) (−17.38) (−18.32)(B/A)·τ c − −12.98 −14.03 −15.05 −8.69

( −8.15) (−8.79) (−9.38) (−5.80)(1 − τ ps)/(1 − τ pb) ? −0.49 0.19 0.50

(−3.00) (1.00) (2.53)(B/A)·(1 − τ ps)/(1 − τ pb) + 5.18 3.38 3.07

(8.06) (5.10) (4.66)Yield ? −18.18 −8.04

(−9.63) (−4.17)(τ d − τ cg )/(1 − τ cg ) ? −2.41 −1.58

(−9.38) (−6.12)Yield·(τ d − τ cg )/(1 − τ cg ) + 88.28 69.73

(13.37) (10.50)βMKT + 0.46 0.44 0.42 0.39 0.26

(12.25) (12.13) (11.57) (10.74) (6.89)β SMB + 0.49 0.48 0.45 0.44 0.31

(21.04) (21.02) (19.60) (18.73) (13.00)βHML + 0.16 0.12 0.12 0.13 0.21

(19.40) (5.50) (5.53) (5.99) (9.33)ln(Dispersion) + 0.29 0.28 0.28 0.29 0.30

(27.10) (26.56) (26.89) (26.91) (27.91)LTG + 6.71 5.54 5.21 4.97 6.08

(21.93) (18.48) (16.44) (15.26) (18.32)

Fixed effects None None None None IndustryAdj. R2 17.02% 21.77% 22.10% 22.80% 26.65%

Recent evidence suggests that the correlations between certain risk prox-ies and the implied cost of equity vary significantly across different models(e.g., Botosan and Plumlee [2005], Guay, Kothari, and Shu [2005], Dhaliwalet al. [2005]). To understand how the effect of leverage and taxes variesacross the implied cost of equity estimates, we estimate the full model, in-cluding industry effects, separately for r gls , r ct , r ojn, and r mpeg . Results are


T A B L E 5Regression of Individual Implied Equity Premiums on Leverage and Personal and Corporate Tax

Variables

This table presents regression results from estimating a pooled time-series cross-sectional re-gression using all observations available for each cost of equity estimate over 1982 through2004. Industry fixed effects were included in the estimation (not reported). B/A is the mar-ket value of debt divided by market value of assets at the end of year t–1. τ c equals thesimulated marginal tax rate before financing for year t–1. (1 − τ ps)/(1 − τ pb) is the per-sonal tax penalty associated with debt. Yield is equal to the last annualized quarterly divi-dend paid in year t–1 divided by the stock price at the beginning of the month. (τ d − τ cg )/(1 − τ cg ) is the dividend tax penalty. βMKT , β SMB , and βHML are the Fama and French risk fac-tors estimated using at least 24 and up to 60 monthly returns ending in June of year t. Dispersionequals the standard deviation of analyst estimates for year t earnings divided by the consensusforecast for year t earnings. LTG equals the mean long-term growth forecast available in Juneof year t. t-statistics are reported in parentheses.

Dependent variable = cost of equity

r gls r ct r ojn r mpeg

B/A + 19.49 −0.03 1.48 3.35(9.89) (−0.02) (1.30) (2.11)

τ c ? −17.01 −17.01 −5.28 −12.24(−31.43) (−26.72) (−13.87) (−22.92)

(B/A)·τ c − −25.68 −1.06 −4.96 −2.82(−11.50) (−0.41) (−3.03) (−1.23)

(1 − τ ps)/(1 − τ pb) ? 4.36 1.99 −1.70 −0.61(11.00) (4.36) (−7.90) (−2.03)

(B/A)·(1 − τ ps)/(1 − τ pb) + −0.55 5.65 4.40 4.22(−0.44) (3.89) (6.11) (4.19)

Yield ? −35.01 1.36 14.33 −0.33(−9.20) (1.44) (6.84) (−0.11)

(τ d − τ cg )/(1 − τ cg ) ? −3.30 1.52 0.69 −0.21(−6.44) (2.56) (2.43) (−0.52)

Yield·(τ d − τ cg )/(1 − τ cg ) + 126.81 2.21 61.36 92.57(9.56) (1.44) (8.45) (9.15)

βMKT + 0.48 0.86 0.27 0.47(6.65) (10.37) (6.60) (14.91)

β SMB + 0.26 0.71 0.37 0.54(5.63) (13.26) (14.22) (14.91)

βHML + −0.06 −0.35 0.14 0.10(−1.49) (−7.18) (5.84) (3.04)

ln(Dispersion) + −0.30 −0.74 0.41 0.71(−17.97) (−38.00) (34.38) (42.71)

LTG −5.87 5.53 11.94 4.08(−10.38) (8.19) (32.98) (8.02)

N = 22,873 22,769 20,535 20,375Adj. R2 24.52% 21.31% 26.01% 27.40%

reported in table 5. The coefficient on the interaction between B/A and τ c

ranges from −1.06 to −25.68. When rgls and rojn are the dependent variables,the coefficient on (B/A)·τ c is negative and significant; however, when r ct

and r mpeg are the dependent variables, the coefficient on (B/A)·τ c is nega-tive but insignificant. Part of this inconsistency may be due to the variation


in sample compositions. For example, we do not require positive earningsforecasts to estimate r gls and r ct , which is a necessary condition to estimateboth r ojn and r mpeg . When the regressions are constrained to the subsampleof firms with nonmissing values for all cost of equity estimates, the coefficienton (B/A)·τ c is insignificant only when r mpeg is the dependent variable. Wetest for the effect of investor level taxes on the equity risk premium fromleverage by interacting B/A with (1 − τ ps)/(1 − τ pb). We predict the coef-ficient on this term to be positive. When the cost of equity is specified asr ct , r ojn, or r mpeg , the coefficient is positive and significant and ranges from4.22 to 5.65. However, when r gls is the dependent variable, the coefficientestimate is insignificant (coefficient = −0.55, t-statistic = −0.44).

Using the average cost of equity estimate, the results provide consistentsupport for H2 and H3; however, these hypotheses are not uniformly sup-ported by the individual models. Notably, we obtain insignificant results forpersonal tax effects when the dependent variable is r gls , and insignificantresults for corporate tax effects when the dependent variable is r ct and r mpeg .Botosan and Plumlee [2005] find that the Gebhardt, Lee, and Swaminathan[2001] specification has unstable associations with risk proxies, which maypartly explain this result. At a minimum, the results in our study and inBotosan and Plumlee [2005] and Guay, Kothari, and Shu [2005] illustratethe potential risk of relying on a single implied cost of equity estimate forempirical tests.

A significant concern using a pooled specification is that cross-correlationin the residuals may bias the standard errors downward. Annual regressionsare typically used to address this issue. In our context, annual regressionsrely on variation in dividend policies across firms to estimate the effect ofinvestor level taxes on the equity risk premium associated with leverage. Ifcross-sectional variation in the personal tax penalty of debt is found to haveno effect on the pricing of leverage, we are likely to conclude that time seriesvariation in statutory tax rates drives the relation.

We estimate annual cross-sectional regressions for the full model with in-dustry effects and test our hypotheses using the time-series of coefficientestimates. The results are reported in table 6 for all cost of equity estimates.The coefficient on (B/A)·τ c is negative and significant within all cost of eq-uity regressions, except when r ct is the dependent variable, and is generallylarger than the coefficient obtained using a pooled regression. This suggeststhat cross-sectional variation in corporate tax rates across firms matters toinvestors, and further supports the notion that the cost of equity is decreas-ing in the corporate tax benefit from debt, reinforcing the results in tables 4and 5.

Contrary to the results in tables 4 and 5, however, the coefficient on(B/A)·(1 − τ ps)/(1 − τ pb) is insignificantly different from zero in all mod-els. It is important to note that within a particular year, the statutory tax ratesused to estimate (1 − τ ps)/(1 − τ pb) do not vary. As discussed above, onlypooled regressions without fixed year effects incorporate variation in statu-tory tax rates into the personal tax penalty measure. Cross-sectional variation


T A B L E 6Annual Regressions of Implied Equity Premiums on Leverage and Personal and Corporate Tax Variables

This table presents regression results from an annual cross-sectional regression using all obser-vations available for each cost of equity estimate from 1982 through 2004. Industry fixed effectswere included in the estimation (not reported). B/A is the market value of debt divided bymarket value of assets at the end of year t–1. τ c equals the simulated marginal tax rate beforefinancing for year t–1. (1 − τ ps)/(1 − τ pb) is the personal tax penalty associated with debt. Yieldis equal to the last annualized quarterly dividend paid in year t–1 divided by the stock priceat the beginning of the month. βMKT , β SMB , and βHML are the Fama and French risk factorsestimated using at least 24 and up to 60 monthly returns ending in June of year t. Dispersionequals the standard deviation of analyst estimates for year t earnings divided by the consensusforecast for year t earnings. LTG equals the mean long-term growth forecast available in Juneof year t. t-statistics are based on the time-series of estimated coefficients and are reported inparentheses.

Dependent variable = cost of equityr avg r gls r ct r ojn r mpeg

B/A + 10.08 17.98 −2.05 11.10 16.01(4.33) (2.15) (−0.28) (4.73) (4.58)

τ c ? −3.75 −9.99 −17.63 −4.33 −10.07(−5.03) (−3.41) (−5.28) (−4.40) (−6.50)

(B/A)·τ c − −13.29 −32.55 1.36 −14.43 −13.62(−2.83) (−2.69) (0.11) (−3.57) (−2.51)

(1 − τ ps)/(1 − τ pb) ? 1.54 5.19 2.24 −1.70 −0.03(2.37) (4.41) (1.95) (−2.32) (−0.04)

(B/A)·(1 − τ ps)/(1 − τ pb) + 0.69 2.32 6.23 −0.13 −2.20(0.44) (0.61) (1.69) (−0.07) (−0.79)

Yield + 14.82 −7.35 −1.52 29.44 22.76(8.14) (−1.57) (−0.45) (14.17) (7.50)

βMKT + 0.42 0.52 0.88 0.44 0.68(4.33) (4.50) (6.71) (3.90) (4.57)

β SMB + 0.48 0.37 0.65 0.55 0.81(8.96) (2.79) (5.74) (9.19) (9.99)

βHML + 0.07 −0.13 −0.32 0.04 −0.08(1.22) (−1.01) (−2.15) (0.62) (−1.18)

ln(Dispersion) + 0.34 −0.24 −0.67 0.43 0.74(16.47) (−4.34) (−8.99) (14.91) (15.56)

LTG + 5.97 −5.88 4.33 11.94 3.15(7.27) (−5.47) (3.08) (11.83) (3.11)

Average Adj. R2 32.20% 24.76% 23.70% 32.26% 32.39%

is driven only by dividend policies of the sample firms. The cross-sectionalresults for the personal tax effect contrast with Graham [1999] who findsthat personal taxes affect capital structure decisions. One possible explana-tion for this difference is that information used for making capital structuredecisions and pricing leverage risk is somehow different between managersand equity investors. The lack of findings for the personal tax effect in thecross-section may also be due to measurement error, a lack of sufficientcross-sectional variation in the personal tax penalty in our sample, or theexistence of tax clienteles for the firm’s equity and debt that mitigate theeffect of personal level taxes on the equity risk premium from leverage.


In general, the results suggest that as the firm-specific expected tax benefitfrom debt increases, the premium demanded by investors for a given amountof leverage falls. The personal tax penalty associated with debt also appears toaffect the leverage-related equity risk premium. When moving from pooledregressions to annual regressions, the effect of corporate taxes appears tobecome stronger while the effect of personal taxes becomes insignificant.

4.3 ECONOMIC INTERPRETATION AND SIGNIFICANCE

Equation (12) represents the marginal effect of corporate taxes on theassociation between leverage and the cost of equity as a function of the costof capital for the all-equity firm, the personal tax penalty on interest income,and the cost of debt. We use this expression to assess the reasonableness ofthe coefficient estimates obtained from the regressions by assuming valuesfor the parameters based on our sample and comparing the results with theempirical estimates.

To estimate K U , the cost of capital for the all-equity firm, we run thefollowing regression based on equation (8):

ravg = α0 + α1 B/A + ε. (18)

Following Modigliani and Miller [1958], we interpret the intercept as anestimate of K U . In our sample, this value is 11.43%. To obtain the valuefor (1 − τ ps)/(1 − τ pb), we use the sample mean from table 2, which is1.428. For the value of r , which is the yield on corporate debt, we use thetime-series average of Aaa rated Moody’s seasoned bond yields over the years1982 through 2004, resulting in a value of 8.56%. Utilizing equation (12), weobtain a predicted value of −7.76 for the marginal effect of corporate taxeson the association between leverage and the cost of equity. Finally, we adjustfor the fact that our measure of financial leverage uses the market value ofassets (A) in the denominator rather than the market value of equity (S).Because we add the book value of debt (B) to the denominator, our measureof leverage is smaller than the measure used to derive equation (12), andthe coefficients we estimate will be larger than what is predicted by theory.To adjust for our measure, we multiply −7.76 by the coefficient δ, which sat-isfies the following equation: (B/S) = δ(B/A). B/A is equivalent to B/(B +S), thus, δ is equal to (1 − B/S) −1. δ will vary across firms, but for themedian firm with B/S equal to 0.215, δ is approximately equal to 1.27. Thetheoretical coefficient on the interaction between the marginal tax rate andthe debt-to-value ratio for the average firm is –7.76 multiplied by 1.27, whichis equal to –9.86. Thus, the estimated value of –8.69 in column (2) of table 4is plausible given reasonable values for leverage, corporate and personaltaxes, and the cost of debt and equity.

We obtain similar evidence on the reasonableness of the personal taxeffect. Equation (13) expresses the theoretical coefficient on the interactionbetween B/S and (1 − τ ps)/(1 − τ pb), K U (1 − τ c). Using the estimated valueof K U obtained above and the sample average simulated marginal tax ratebefore financing of 35.8%, the predicted coefficient on the interaction is


7.34. Thus, the coefficient estimate of 3.07 obtained in column (5) of table 4appears to be reasonable, although less than that predicted by theory.

To gauge the economic significance of the tax effect, we consider thecoefficients reported in column (5) of table 4 and assume a one standarddeviation change in the debt-to-value ratio equal to 15%. Let τ ps = τ pb, thus[(1 − τ ps)/(1 − τ pb)] = 1. If τ c = 0, the change in leverage increases thecost of equity by 125 basis points [(5.31 + 3.07) ·0.15].15 If τ c is equal tothe present top marginal corporate tax rate of 35% and personal taxes donot change, the interest deduction benefit obtained from the additionaldebt reduces the cost of equity by 46 basis points (−8.69·0.35·0.15). On theother hand, if corporate taxes are held static, and the personal tax penaltyis increased to the recent level of 1.45 within our sample, the change inleverage will increase the cost of equity by an additional 21 basis points(3.07·0.45·0.15).

4.4 SENSITIVITY ANALYSES

4.4.1. Bankruptcy Costs and Earnings Variability. It is likely that the simu-lated corporate tax rates that we use to define τ c are correlated with thefinancial health of the firm. For example, if a firm expects to incur lossesover the next several periods, this both reduces its marginal tax rate estimateand increases the likelihood of bankruptcy. Thus, we examine the sensitivityof the results controlling for potential distress costs. We proxy for the costof financial distress using Z-Score, which is based on an alternative specifica-tion of the original Altman [1968] Z -score as described in Altman [2000].We define Z-Score as [6.56·(working capital/total assets) + 3.26·(retainedearnings/total assets) + 6.72·(EBIT/total assets) + 1.05·(book value ofequity/book value of liabilities)].16 Z-Score is constructed such that it is de-creasing in financial distress and is positively correlated with estimates ofthe firm’s marginal tax rate (see panel B of table 3). We interact Z-Score withB/A to control for the effects of financial distress on the association betweenleverage and the cost of equity. If the effect of leverage on the firm’s costof equity is increasing in financial distress, we expect the coefficient on theinteraction term to be negative.

Simulated marginal corporate tax rates incorporate information on his-torical earnings variability. Thus, there is also a potential that the simu-lated tax rates used in this study capture some aspect of operating risk notcaptured by our risk proxies. For the subsample of firm-year observationswith sufficient data (18,527 observations), panel B of table 3 shows that the

15 Based on equation (17), the total coefficient on B/A is equal to θ1 + θ2 ·τ c + θ3 ·(1 −τ ps)/(1 − τ pb).

16 We exclude the specification of Z -score that includes a term for asset turnover (sales/totalassets) because strong positive correlations between the Z -score measure and cost of capitalresult. Altman [2000] explains that the Z -score is highly sensitive to industry membershipwhen asset turnover is included, and that this revised model performs substantially similar tothe original Z -score model.


correlation coefficient between the standard deviation of earnings beforeinterest and taxes over the last five years, denoted as σ(EBIT), and the sim-ulated tax rate before (after) financing is −0.309 (−0.289). To control forthe effect of operating risk on the pricing of leverage, we include σ(EBIT)and the interaction between B/A and σ(EBIT) in the model.

The reduced sample in which both Z-Score and σ(EBIT) are availablecontains 18,527 observations where r avg is the dependent variable. We es-timate equation (17) after adding Z-Score and σ(EBIT) and their interac-tions with B/A to the model. Regression results (not tabulated) indicatethat Z-Score is negatively related to the cost of equity (coefficient −0.04,t-statistic = −3.76), consistent with the cost of equity being lower for firmsin better financial health. The effect of bankruptcy costs on the pricing ofleverage is insignificantly different from zero (coefficient −0.17, t-statistic =−1.34). The association between σ(EBIT) and the r avg is positive and signif-icant, as expected (coefficient = 6.76, t-statistic = 9.59). The interaction be-tween B/A and σ(EBIT) is also positive and significant (coefficient = 18.46,t-statistic = 3.16), which suggests that the equity risk premium associatedwith leverage is increasing in the operating risk of the firm. Most importantly,we note that including the effects of bankruptcy costs and operating risk inthe model does not qualitatively change the results concerning the effectof corporate taxes. Specifically, the coefficient on the interaction betweenB/A and τ c remains negative and significant in this subsample (coefficient =−13.79, t-statistic = −3.70). This evidence suggests that the effect of τ c onthe association between leverage and the cost of equity does not arise fromits correlation with financial distress or operating risk.

4.4.2. Alternative Proxies for Leverage and Tax Rates. We next examine thesensitivity of our results to alternative measures of leverage and corporatetax rates. The theoretical measure of leverage used by Modigliani and Miller[1958] is the market value of debt divided by the market value of equity.The primary measure of financial leverage used in our study, B/A, is long-term debt divided by the market value of assets. We adopt this specificationbecause it is frequently used in the empirical literature to proxy for thecapital structure of the firm. Leverage ratios using book value of equityor assets in the denominator are also used. Our primary measure of τ c isthe simulated marginal tax rate before financing as described in Graham[1996a]. We utilize this measure because it is more likely to capture the taxbenefit of a firm’s existing capital structure. Marginal tax rate proxies basedon taxable income after financing are more frequently used, but are moreappropriate for examining incremental financing decisions.

To provide comprehensive evidence on the relation among taxes, lever-age, and the cost of equity capital, we compare results obtained using fourestimates of leverage and three estimates of the marginal corporate taxrate.17 The numerator in all measures of leverage is the book value of

17 The results are not tabulated in the paper but are available on request.


long-term debt, which is used to approximate its market value consistentwith prior research. B/AM (B/AB) is equal to long-term debt divided bymarket (book) value of assets. B/S M (B/S B) is equal to long-term debt di-vided by market (book) value of stockholders’ equity.18 Our three proxiesfor τ c include the simulated marginal tax rates before and after financingand the trichotomous marginal tax rate described in Shevlin [1990]. Thetrichotomous marginal tax rate is equal to the top marginal corporate taxrate when pretax income is positive and NOLs are zero, one-half the topmarginal corporate tax rate if the firm has either negative pretax incomeor NOLs, but not both, and zero if the firm has both negative pretax in-come and NOLs. We test the sensitivity of our results across these alternativemeasures using both pooled and annual regressions.

When τ c is defined as the simulated marginal tax rate before financing,the interaction between leverage and τ c is negative and significant for allmeasures of leverage except B/S B , which is negative and only marginallysignificant. When τ c is defined as the simulated marginal tax rate after fi-nancing, the interaction between leverage and τ c is significant and in thepredicted direction only when leverage is defined as B/AB . A similar pat-tern emerges when τ c is defined as the trichotomous marginal tax rate. Weobtain a qualitatively similar set of results for the marginal tax rate proxies us-ing annual regressions. The conflicting evidence obtained using alternativemarginal tax rate proxies is related to Graham, Lemmon, and Schallheim[1998], who find that marginal tax rates before (after) financing are posi-tively (negatively) related to the firm’s existing capital structure. If marginaltax rate proxies based on earnings after financing explain incremental fi-nancing decisions but do not explain existing capital structures consistentwith theory, then they may also be unable to capture the tax benefit of debtaccruing to equity investors.

The interaction between (1 − τ ps)/(1 − τ pb) and leverage is positive andsignificant for all specifications of leverage in pooled regressions. When werun annual regressions, the interactions between leverage and (1 − τ ps)/(1 − τ pb) are positive and significant when B/E B or B/E M are used as themeasure of leverage, and weakly significant when B/AB is used as the mea-sure of leverage. This contrasts with our earlier results that found that thepersonal tax penalty had no effect on the association between leverage andthe cost of equity in cross-sectional tests. While we do not have an expla-nation for these results, it does suggest the importance of considering theeffect of leverage and taxes across a multitude of measures.

4.4.3. Addressing the Marginal Investor. In constructing (1 − τ ps)/(1 −τ pb), we assume that the marginal investor in the firm’s debt and equity is afully taxable individual. To the extent that the marginal investor is not subjectto individual tax rates, our proxy for the personal tax penalty associated withdebt, (1 − τ ps)/(1 − τ pb), is measured with error. Prior research has used

18 Note that B/AM is the leverage measure used throughout this study.


the percentage of institutional ownership to proxy for the likelihood thatthe marginal investor in the firm’s equity is not an individual (e.g., Ayers,Lefanowicz, and Robinson [2003, 2004]). In our study, τ ps is a weightedaverage of tax rates on dividend and capital gains income for an individualinvestor. Although there is wide variation in the tax status of institutionalinvestors, we expect that institutions will face a lower τ ps than individualson average.19 Thus, our estimate of (1 − τ ps)/(1 − τ pb) understates thepersonal tax penalty associated with debt when institutions are the marginalinvestor in equity.

To test whether institutional ownership improves the ability of (1 − τ ps)/(1 − τ pb) to capture the personal tax penalty of the marginal investors, weinteract (B/A)·(1 − τ ps)/(1 − τ pb) with institutional ownership for the sub-sample of firms with available data.20 If (1 − τ ps)/(1 − τ pb) is understatedwhen the marginal equity investor is not an individual, the coefficient onthe interaction between B/A, (1 − τ ps)/(1 − τ pb), and institutional owner-ship should be positive. The estimated coefficient on this interaction usingpooled regressions is 1.63 (t-statistic = 2.77), which suggests that the per-sonal tax penalty associated with debt is increasing in institutional owner-ship. When the interaction term between (B/A)·(1 − τ ps)/(1 − τ pb) andinstitutional ownership is included in the model, the coefficient on (B/A)·(1 − τ ps)/(1 − τ pb) becomes insignificant. Finally, the coefficient on the in-teraction between (B/A), (1 − τ ps)/(1 − τ pb), and institutional ownershipusing cross-sectional regressions is only 0.58 (t-statistic = 0.85) and suggeststhat cross-sectional specifications are not improved by including a proxy forthe tax status of the marginal investor.

We also examine the sensitivity of our results to the assumption that themarginal investor in the firm’s debt faces the top marginal tax rate forindividuals. Poterba [1989] and Graham [1999] utilize the relation betweentaxable and nontaxable issues to estimate the marginal tax rate implied bythe relative yields. Following this research, we redefine t pb as (Rtaxable −Rtax-free)/R taxable , where R taxable is the yield on one-year Treasury issues, andRtax-free is the yield on one-year prime grade tax-exempt municipal bonds.21

The results (not tabulated) are qualitatively similar using this alternativespecification and our inferences on the effect of personal taxes on the equityrisk premium associated with leverage are unchanged.

4.4.4. The Effect of Entity Level Risk. Scholes et al. [2005] show that themarginal effect of taxes on the expected return of an asset is a function

19 For example, tax-exempt institutions generally pay no tax and corporate institutions candeduct 70% of dividends received from income.

20 Due to data availability, this sample covers 10,019 firm-years from 1989 through 2001.21 We use the implicit rates reported in Graham [1999, p. 158] through 1996. These are:

40.7% from 1982 through 1986, 33.1% in 1987, 28.7% from 1988 through 1992, and 29.6%from 1993 through 1996. For 1997 through 2004, we calculate the implicit tax rate as in Poterba[1989] using monthly observations on one-year Treasury and municipal bond yields. FollowingGraham [1999], we average the monthly implicit tax rates within tax regime and estimate theimplicit tax rate as 28.55% for 1997 through 2002, and 16.0% for 2003 and 2004.


of the asset’s underlying risk. This is captured in equations (12) and (13),which show that the marginal effect of corporate and investor level taxes onthe equity risk premium from leverage is a function of the operating risk ofthe firm, as measured by K U . To examine whether the effects of corporateand investor level taxes on the equity risk premium from leverage are afunction of firm risk, we sort firms into three equal groups each year basedon their value of σ(EBIT). We choose to sort firms by σ(EBIT) as that is areasonable approximation of the operating risk of the firm before capitalstructure decisions are made. We then estimate equation (17) using bothpooled and annual regressions.

We predict that the coefficient on the interaction between B/A andτ c (B/A and (1 − τ ps)/(1 − τ pb)) will be decreasing (increasing) as the oper-ating risk increases. The evidence generally supports these predictions (re-sults not tabulated). For the pooled regression, the coefficient on (B/A)·τ c

is 6.42 (t-statistic = 2.51) for the low σ(EBIT) group. It decreases to −6.44(t-statistic = −2.16) for the medium σ(EBIT) group and further to −15.05(t-statistic = −5.63) for the high σ(EBIT) group. The coefficient on (B/A)·(1 − τ ps)/(1 − τ pb) is insignificant for both the low and medium σ(EBIT)groups, but increases to 5.30 (t-statistic = 3.92) for the high σ(EBIT) group.We find a similar pattern in annual regressions. Thus, the evidence is gen-erally consistent with the proposition that the effect of taxes on the equityrisk premium from leverage is increasing in firm risk.

4.4.5. Fiscal Year-ends. Finally, we examine whether our results are ro-bust to the subsample of firms with December fiscal year-ends. This is po-tentially important, as we calculate the implied cost of capital at a fixeddate and variation in firm-specific information since the last financial state-ment release may bias our estimates of the cost of equity for some firms.The results for both corporate and personal taxes are qualitatively similarto those presented earlier using both pooled and annual cross-sectionalregressions.

5. Conclusions

Expanding Modigliani and Miller [1958, 1963], it can be shown that thetheoretical association between leverage and the cost of equity capital isdecreasing in the corporate tax benefit from debt and increasing in the per-sonal tax penalty associated with debt. Using estimates for the ex ante costof equity capital implied by accounting-based valuation models, we investi-gate the effects of corporate and personal taxes on the association betweenfinancial leverage and the cost of equity. We find that simulated corporatemarginal tax rates before financing consistently explain the association be-tween leverage and the cost of equity. Although the results are sensitive tothe cost of equity and leverage estimates used, we interpret the overall ev-idence to be consistent with the prediction that the corporate tax benefitreduces the leverage-related risk premium demanded by equity investors.


In addition, we find that when the marginal tax rate is based on earn-ings after financing, corporate taxes do not appear to affect the associationbetween leverage and the cost of equity. These tax rates best capture thetax benefit from incremental financing choices. Thus, our results are notsurprising if proxies for the marginal tax rate after financing do not capturethe tax benefit of the firm’s existing capital structure.

Evidence on the effect of personal taxes on the equity risk premium fromleverage depend on the specification of the model. In cross-sectional speci-fications, the effect of the personal tax penalty on the association betweenleverage and the cost of equity is generally small or nonexistent. However,if we allow the proxy for the personal tax penalty to take into account tem-poral variation in statutory tax rates using a pooled regression, we find thatthe effect of the personal tax penalty on the association between leverageand the cost of equity is generally positive and significant. This suggests thattime-series variation in statutory tax rates, and not cross-sectional variationdue to dividend policy, explains the relation.

Overall, this paper provides evidence that the association between lever-age and the cost of equity is affected by corporate and investor level taxes.The results are generally consistent with prior research, which shows thatcapital structure decisions are related to the firm-specific magnitude of thecorporate tax benefit of debt and the personal tax penalty associated withdebt. This paper contributes to the large body of research that addressesthe question of whether taxes affect pretax returns required by investors.We exploit recent developments in the accounting literature to derive exante estimates of the cost of capital and provide an empirical foundation forunderstanding the impact of managers’ capital structure decisions on firmvalue and the cost of equity capital.

APPENDIX

Models Used to Estimate the Cost of Equity Capital

The following definitions are common to the four models. Specific as-sumptions and modifications to these variables are described with themodel.

P t = price per share of common stock in June of year t as reportedby I/B/E/S

Bt = book value at the beginning of the year divided by the numberof common shares outstanding in June of year t

DPS0 = dividends per share paid during year t–1EPS0 = actual earnings per share reported by I/B/E/S for year t–1LTG = consensus long-term growth forecast reported in June of

year tFEPSt+i = forecasted earnings per share for year t+i. FEPS1 and FEPS2

are equal to the one and two-year-ahead consensus EPS


forecasts reported in I/B/E/S in June of year t. FEPS3 isequal to the three-year-ahead consensus EPS forecast whenavailable, and FEPS2·(1 + LTG) when not available.

k = expected dividend payout ratio, calculated as DPS0/EPS0. IfEPS0 ≤ 0, then k is equal to 6% of the total assets at thebeginning of year t

r j = implied cost of equity estimate for each of the four models.r rf = risk-free rate equal to the yield on a 10-year Treasury note in

June of year t.

Gebhardt, Lee, and Swaminathan [2001]

Pt = Bt + FROEt+1 − rgls

(1 + rgls)Bt + FROEt+2 − rgls

(1 + rgls)2 Bt+1 + TV

TV =T−1∑i=3

FROEt+i − rgls

(1 + rgls)iBt+i−1 + FROEt+T − rgls

rgls(1 + rgls)T−1 Bt+T−1

where:

FROEt+i = forecasted return on equity (ROE) for period t+i. For yearsone through three, this variable is equal to FEPSt+i/Bt+i−1.Beyond year three, FROEt+i is a linear interpolation to the in-dustry median ROE. Industry median ROE is defined as themoving median ROE for the prior 5–10 years for the firmsindustry (excluding loss firm-years). Industries are definedusing the 48 classifications in Fama and French [1997]

Bt+i = Bt+i−1 + FEPSt+i · (1 − k)T = forecast horizon. T = 12.

Claus and Thomas [2001]

Pt = Bt + ae1

(1 + rct)+ ae2

(1 + rct)2 + ae3

(1 + rct)3 + ae4

(1 + rct)4

+ ae5

(1 + rct)5 + ae5(1 + gae)(rct − gae)(1 + rct)5

where:

aet+i = abnormal earnings calculated as FEPSt+I − r ct ·Bt . For year +3,+4, and +5, FEPSt+i is equal to the consensus forecast for thatyear, if available, otherwise FEPSt+i = FEPSt+i−1·(1 + LTG)

Bt+i = Bt+i−1 + k·FEPSt+i . k is assumed to be 0.5 in Claus and Thomas[2001]

g ae = growth in abnormal earnings, calculated as r rf − 0.03.


Gode and Mohanram [2003]

rojn = A +√

A2 +(

FEPSt+1

Pt

)(g2 − ((rrf − 0.03))

where

A = 0.5(

(r f − 0.03) + DPSt+1

Pt

)and

g2 = (FEPSt+2 − FEPSt+1)FEPSt+1

g 2 = short-term growth rate defined as (STG + LTG)/2. STG isequal to (FEPSt+2/FEPSt+1 − 1)

DPSt+1 = DPS0

Note: This model is based on Ohlson and Juettner-Narouth [2005]. It re-quires FEPSt+1 > 0 and FEPSt+2 > 0.

Easton [2004]

Pt =(

FEPSt+2 + rmpeg DPSt+1 − FEPSt+1

r 2mpeg

)

DPSt+1 = DPS0

Note: This model requires FEPSt+2 ≥ FEPSt+1 > 0.

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