THE JOURNAL OF FINANCE•VOL.LV,NO.5•OCT.2000
关于学校的对联
How Big Are the Tax Benefits of Debt?
JOHN R.GRAHAM*
ABSTRACT
I integrate under firm-specific benefit functions to estimate that the capitalized
tax benefit of debt equals9.7percent of firm value~or as low as4.3percent,net of
personal taxes!.The typical firm could double tax benefits by issuing debt until the
marginal tax benefit begins to decline.I infer how aggressively a firm us debt by
obrving the shape of its tax benefit function.Paradoxically,large,liquid,profit-
able firms with low expected distress costs u debt conrvatively.Product mar-
ket factors,growth options,low ast collateral,and planning for future expenditures青春梦想
lead to conrvative debt usage.Conrvative debt policy is persistent.
D O TH
E TAX BENE
F ITS of debt affect corporate financing decisions?How much do they add to firm value?The questions have puzzled rearchers since the work of Modigliani and Miller~1958,1963!.Recent evidence indicates that tax benefits are one of the factors that affect financing , MacKie-Mason~1990!,Graham~1996a!!,although opinion is not unanimous on which factors are most important or how they contribute to firm value ~Shyam-Sunder and Myers~1998!,Fama and French~1998!!.巩县窑
Rearchers face veral problems when they investigate how tax incen-tives affect corporate financial policy and firm value.Chief among the problems is the difficulty of calculating corporate tax rates due to data prob-lems and the complexity of the tax code.Other challenges include quantify-ing the effects of interest taxation at the personal level and understanding the bankruptcy process and the attendant costs of financial distress.In this *Graham is at the Fuqua School of Business,Duke University.Early conversations with Rick Green,Eric Hughson,Mike Lemmon,and S.P.
Kothari were helpful in formulating some of the ideas in this paper.I thank Peter Fortune for providing the bond return data and Eli Ofek for supplying the managerial entrenchment data.I also thank three referees for detailed comments;also,Jennifer Babcock,Ron Bagley,Alon Brav,John Campbell,John Chalmers,Bob Dammon,Eugene Fama,Roger Gordon,Mark Grinblatt,Burton Hollifield,Steve Huddart, Arvind Krishnamurthy,Rich Lyons,Robert MacDonald,Ernst Maug,Ed Maydew,Roni Michaely, Phillip O’Conner,John Persons,Dick Rendleman,Oded Sarig,RenéStulz~the editor!,Bob Taggart,S.Viswanathan,Ralph Walkling,and Jaime Zender;minar participants at Carnegie Mellon,Chicago,Duke,Ohio State,Rice,the University of British Columbia,the University of North Carolina,Washington University,William and Mary,and Yale;minar participants at the NBER Public Economics and Corporate workshops,the National Tax Association annual conference,the American Economic Association meetings,and the Eighth Annual Conference on Financial Economics and Accounting for helpful suggestions and feedback.Jane Laird gathered the state tax rate information.All errors are my own.This paper previously circulated under the title“tD or Not tD?Using Benefit Functions to Value and Infer the Costs of Interest Deductions.”
1901
1902The Journal of Finance
paper I primarily focus on calculating corporate tax benefits.I develop a new measure of the tax benefits of debt that provides information about not just the marginal tax rate but the entire tax benefit function.
A firm’s tax function is defined by a ries of marginal tax rates,with each rate corresponding to a specific level of interest deductions.~Each marginal tax rate incorporates the effects of non-debt tax shields,tax-loss carrybacks, carryforwards,tax credits,the alternative minimum tax,and the probability that interest tax shields will be ud in a given year,bad on the method-ology of Graham~1996a!!.The tax function is generally f lat for small inter-est deductions but,becau tax rates fall as interest expen increas, eventually becomes downward sloping as interest increas.This occurs be-cau interest deductions reduce taxable income,which decreas the prob-ability that a firm will be fully taxable in all current and future states, which in turn reduces the tax benefit from the incremental deductions. Having the entire tax rate function allows me to make three contributions toward understanding how tax benefits affect corporate choices and value. First,I quantify the tax advantage of debt by integrating to determine the area under the tax benefit function.This contrasts with the traditional ap-proach of measuring tax benefits as the product of the corporate tax rate and the amount of debt~Brealey and Myers~1996!!.I estimate that the tax benefit
of interest deductibility equals9.7percent of market value for the typical firm,in comparison to13.2percent according to the traditional ap-proach.When I adjust the tax functions for the taxation of interest at the personal level,the benefit of interest deductibility falls to between four and ven percent of firm value.In certain circumstances,however,the benefits are much larger:Safeway and RJR Nabisco achieved net tax benefits equal to nearly20percent of ast value after they underwent leveraged buyouts. Second,I u the tax rate functions to determine how aggressively firms u debt.I quantify how aggressively a firm us debt by obrving the “kink”in its tax benefit function,that is,the point where marginal benefits begin to decline and therefore the function begins to slope downward.More specifically,I define kink as the ratio of the amount of interest required to make the tax rate function slope downward~in the numerator!to actual interest expen~in the denominator!.If kink is less than one,a firm oper-ates on the downward-sloping part of its tax rate function.A firm with kink less than one us debt aggressively becau it expects reduced tax benefits on the last portion of its interest deductions.If kink is greater than one,a firm could increa interest expen and expect full benefit on the incre-mental deductions;such a firm us debt conrvatively.Therefore,debt conrvatism increas with kink.
I compare this new gauge of how aggressively firms u debt with vari-ables that measure the costs
of debt,to analyze whether corporate behavior is consistent with optimal capital structure choice.Surprisingly,I find that the firms that u debt conrvatively are large,profitable,liquid,in stable industries,and face low ex ante costs of distress;however,the firms also have growth options and relatively few tangible asts.I also find that debt
How Big Are the Tax Benefits of Debt?1903 conrvatism is persistent,positively related to excess cash holdings,and weakly related to future acquisitions.My results are consistent with some firms being overly conrvative in their u of debt.Indeed,44percent of the sample firms have kinks of at least ,they could double interest deductions and still expect to realize full tax benefit from their tax deduc-tions in every state of nature!.
Third,I estimate how much value a debt-conrvative firm could add if it ud more debt.I conjecture that,in equilibrium,the cost of debt function should interct the tax benefit function on its downward-sloping portion. This implies that firms should have~at least!as much debt as that associ-ated with the kink in the benefit function.Levering up to the kink,the typical firm could add15.7percent~7.3percent!to firm value,ignoring ~considering!the personal tax penalty.Combined with Andrade and Kaplan’s ~1998!conclusion that financial distress costs equal between10and23per-cent of firm value,current debt policy is justified if levering up increas the pro
bability of distress by33to75percent.Given that only one-fourth of Andrade and Kaplan’s sample firms default within10years,even extreme estimates of distress costs do not justify obrved debt policies.
My analysis is related to rearch by Engel,Erickson,and Maydew~1998!, who u market returns to measure directly the net tax advantage of a debt-like instrument,MIPS~monthly income preferred curities!.For a sample of22large firms issuing MIPS,Engel et al.~1998!estimate that a dollar of “interest”yields a net tax benefit of$0.315in the mid-1990s,at a time when their sample firms faced federal and state taxes of around40percent.This implies a personal tax penalty no larger than21percent~0.21ϭ0.08500.40!. In contrast,I impute the personal tax penalty using the corporate tax rate, the personal tax rate on debt,the personal tax rate on equity,and firm-specific estimates of dividend payout.Although my analysis and that of Engel et al.~1998!u different samples,time periods,and financial cu-rities,if I u the smaller Engel et al.~1998!estimate of the personal tax penalty,the net tax advantage to debt equals ven to eight percent of mar-ket value for my sample.
The paper proceeds as follows.Section I discuss the costs and benefits of debt and describes how I estimate benefit functions.Section II discuss data and measurement issues.Section III quantifies the tax advantage of debt in aggregate and prents ca studies for individual firms.Section IV com
pares the benefit functions to variables measuring the cost of debt.Section V esti-mates the tax savings firms pass up by not using more debt.Section VI concludes.
I.The Costs and Benefits of Debt
权益基金A.Estimating the Tax Costs and Benefits of Debt
牙结石怎么形成的The tax benefit of debt is the tax savings that result from deducting in-terest from taxable earnings.By deducting a single dollar of interest,a firm reduces its tax liability by t C,the marginal corporate tax rate.~Note that t C
1904The Journal of Finance
captures both state and federal taxes.!The annual tax benefit of interest deductions is the product of t C and the dollar amount of interest,r d D,where r d is the interest rate on debt,D.To capitalize the benefit from current and future interest deductions,the traditional approach~Modigliani and Miller ~1963!!assumes that tax shields are as risky as the debt that generates them and therefore discounts tax benefits with r d.If debt is perpetual and interest tax shields can always be ud fully,the capitalized tax benefit of debt simplifies to t C D.
初一下册历史书
Miller~1977!points out that the traditional approach ignores personal taxes.Although interest payments help firms avoid corporate income tax, interest income is taxed at the personal level at a rate t P.Payments to equity holders are taxed at the corporate level~at rate t C!and again at the personal level~at the personal equity tax rate t E!.Therefore,the net benefit of directing a dollar to investors as interest,rather than equity,is
~1Ϫt P!Ϫ~1Ϫt C!~1Ϫt E!.~1!
Equation~1!can be rewritten as t C minus the“personal tax penalty”,t PϪ~1Ϫt C!t E.I u equation~1!to value the net tax advantage of a dollar of interest.Following Gordon and MacKie-Mason~1990!,I estimate t E as~dϩ~1Ϫd!g a!t P,where d is the dividend–payout ratio,g is the proportion of long-term capital gains that are taxable,a measures the benefit of deferring capital gains taxes,and dividends are taxed at t P.
If debt is riskless and tax shields are as risky as the underlying debt,then the after-personal-tax bond rate is ud to discount tax benefits in the pres-ence of personal taxes~Taggart~1991!,Benninga and Sarig~1997!!.If the debt is also perpetual,the capitalized tax benefit of debt is
@~1Ϫt P!Ϫ~1Ϫt C!~1Ϫt E!#r d D
.~2!
~1Ϫt P!r d
Equation~2!simplifies to t C D if there are no personal taxes.In contrast,a Miller equilibrium would imply that expression~2!equals zero.My data assumptions imply that the personal tax penalty partially offts the corpo-rate tax advantage to debt on average,not fully offts it as it would for every firm in a Miller equilibrium~e Section II.A!.
Thus far,I have prented t C as if it is a constant.There are two impor-tant reasons why t C can vary across firms and through time.First,firms do not pay taxes in all states of nature.Therefore,t C should be measured as a weighted average,considering the probabilities that a firm does and does not pay taxes.Moreover,to ref lect the carryforward and carryback provisions of the tax code,this averaging needs to account for the probability that taxes are paid in both the current and future periods.This logic is consistent with an economic interpretation of the marginal tax rate,defined as the prent value tax obligation from earning an extra dollar today~Scholes and Wolfson ~1992!!.To ref lect the interaction between U.S.tax laws and historical and
How Big Are the Tax Benefits of Debt?1905 future tax payments,I estimate corporate marginal tax rat
es with the sim-ulation methods of Graham~1996b!and Graham,Lemmon,and Schallheim ~1998!.The tax rates vary with the firm-specific effects of tax-loss carry-backs and carryforwards,investment tax credits,the alternative minimum tax,nondebt tax shields,the progressive statutory tax schedule,and earn-ings uncertainty.Appendix A describes the tax rate methodology in detail. The cond reason that t C can vary is that the effective tax rate is a func-tion of debt and nondebt tax shields.As a firm increas its interest or other deductions,it becomes less likely that the firm will pay taxes in any given state of nature,which lowers the expected benefit from an incremental de-duction.At the extreme,if a firm entirely shields its earnings in current and future periods,its marginal tax rate is zero,as is the benefit from additional deductions.This implies that each dollar of interest should be valued with a tax rate that is a function of the given level of tax shields.As I explain next, t C defines the tax benefit function,and therefore the fact that t C is a de-creasing function of interest expen affects my estimate of the tax benefits of debt in important ways.
Rather than using equation~2!,I estimate the tax benefits of debt as the area under the tax benefit function.To estimate a benefit function,I first calculate a tax rate assuming that a firm does not have any interest deduc-tions.This first tax rate is referred to as MTR it0%for Firm i in Year t and is the ma
rginal tax rate that would apply if the firm’s tax liability were bad on before-financing income~EBIT,which incorporates zero percent of actual interest expen!.Next,I calculate the tax rate,MTR it20%,that would apply if the firm hypothetically had20percent of its actual interest deductions.I also estimate marginal tax rates bad on interest deductions equal to40, 60,80,100,120,160,200,300,400,500,600,700,and800percent of actual interest expen.~All el is held constant as interest deductions vary,in-cluding investment policy.Nondebt tax shields are deducted before interest.! By“connecting the dots,”I link the quence of tax rates to map out a tax benefit curve that is a function of the level of interest deductions.To derive a net~of personal tax effects!benefit function,I connect a quence of tax benefits that results from running t C through equation~1!.An interest de-duction benefit function can be f lat for initial interest deductions but even-tually becomes negatively sloped becau marginal tax rates fall as additional interest is deducted.1
To estimate the tax-reducing benefit provided by interest deductions for a single firm-year,I integrate to determine the area under a benefit function up to the level of actual interest expen.To estimate the prent value of
1Talmor,Haugen,and Barnea~1985!model benefit functions with debt on the horizontal axis.They arg
关于时间的谜语ue that debt benefit functions can slope ,increasing marginal ben-efits to debt!becau increasing the amount of debt can increa the interest rate and tax benefit faster than it increas the probability of bankruptcy.If the tax schedule is progressive, my benefit functions never slope upward becau I plot interest on the horizontal axis,so my functions already include any effect of interest rates changing as debt ,becau of rising interest rates it may take only an80percent increa in debt to double interest deductions!.
1906The Journal of Finance
such benefits~from Year tϩ1through`!,rather than assuming debt is perpetual as in equation~2!,I capitalize annual tax benefit estimates from a time ries of functions.For example,I estimate the prent value benefit at year-end1990for Firm i by doing the following:~1!using historical data through year-end1990to derive an interest deduction benefit function for Firm i in1991~which is tϩ1in this ca!and integrating under the func-tion to estimate the net tax-reducing benefit of interest deductions for1991; ~2!still using historical data through1990,I make a projection of the benefit function for1992~tϩ2!and integrate under the expected tϩ2function to estimate the tax-reducing benefit of interest for1992;~3!I repeat the pro-cess in~2!for each Year tϩ3through tϩ10and sum the prent values of the benefits for Years tϩ1through tϩ10.In much of the empirical work, I follow the tr
aditional textbook treatment of valuing tax shields and u Moody’s before-tax corporate bond yield for Year t as the discount rate;and ~4!I invert the annuity formula to convert the10-year prent value into the capitalized value of all current and future tax benefits as of year-end1990. The benefit functions are forward-looking becau the value of a dollar of current-period interest can be affected,via the carryback and carryforward rules,by the distribution of taxable income in future years.In addition, future interest deductions can compete with and affect the value of current tax shields.I assume that firms hold the interest coverage ratio constant at the Year-t value when they are profitable but maintain the Year-t interest level in unprofitable states.2For example,assume that income is$500in Year t and interest deductions are$100.If income is forecast to ri to$600 in tϩ1,my assumption implies that interest deductions ri to$120. Alternatively,if income decreas to$400,interest falls to$80.If income is forecast as negative in tϩ1,interest remains constant at$100~implicitly assuming that the firm does not have sufficient cash to retire debt in un-profitable states!.Likewi,if the firm’s income is forecast to be$400in tϩ1and then negative in tϩ2,Year-tϩ2interest deductions are assumed to be$80.
This approach may misstate the tax benefits of debt if firms can optimize debt policy better than I assume.For example,if firms retire debt in un-profitable future states,Year-t interest deductions have
labordayfewer future deduc-tions to compete with,and so my calculations understate the tax advantage of Year-t debt policy.Likewi,the likelihood increas that Year-t interest deductions will be ud in the near term,and so my calculations understate the tax advantage of Year-t debt policy if~1!a financing pecking order holds; then profitable firms are likely to allow their interest coverage ratios to increa as they realize future profits and so issue less debt in the future;
2When determining capitalized tax benefits,future debt policy affects benefits in future years and,indirectly,the benefits in the current year.With respect to the latter,future interest deductions compete with Year-t deductions through the carryback and carryforward provisions of the tax code.To gauge the importance of my assumptions about future debt policy,I perform an unreported specification check that assumes that firms follow a partial adjustment model ~i.e.,they do not fully adjust their tax shielding ratios in either profitable or unprofitable states!.This has little effect on the numbers reported below.
