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Optimal Capital Structure under Corporate Optimal Capital Structure under Corporate and Personal Taxationand Personal Taxation
Harry DeANGELOHarry DeANGELOUniversity of WashingtonUniversity of Washington
Ronald W. MASULISRonald W. MASULISUniversity of CaliforniaUniversity of California
Securities and Exchange CommissionSecurities and Exchange Commission
Received September 1978, final version received December 1979Received September 1978, final version received December 1979
Outline of PresentationOutline of Presentation
Introduction Introduction Elements of the modelElements of the model Miller’s leverage irrelevancy Miller’s leverage irrelevancy
theoremtheorem Tax shield substitutes for debt Tax shield substitutes for debt
and interior optimum leverageand interior optimum leverage Bankruptcy costs and horse-and-Bankruptcy costs and horse-and-
rabbit stew rabbit stew [continued] [continued]
Testable hypothesesTestable hypotheses Empirical evidenceEmpirical evidence SummarySummary
IntroductionIntroduction
In this paper, a model of corporate leverage choice In this paper, a model of corporate leverage choice is formulated in which corporate and differential is formulated in which corporate and differential personal taxes exist and supply side adjustments by personal taxes exist and supply side adjustments by firms enter into the determination of equilibrium firms enter into the determination of equilibrium relative prices of debt and equity.relative prices of debt and equity.
The presence of corporate tax shield substitutes for The presence of corporate tax shield substitutes for debt such as accounting depreciation, depletion debt such as accounting depreciation, depletion allowances, and investment tax credits is shown to allowances, and investment tax credits is shown to imply a market equilibrium in which each firm has a imply a market equilibrium in which each firm has a unique interior optimum leverage decision (with or unique interior optimum leverage decision (with or without leverage-related costs).without leverage-related costs).
The optimal leverage model yields a number of The optimal leverage model yields a number of interesting predictions regarding cross-sectional interesting predictions regarding cross-sectional and time-series properties of firms’ capital and time-series properties of firms’ capital structures. structures.
Extant evidence bearing on these predictions is Extant evidence bearing on these predictions is examined.examined.
Merton Miller (1977) argues that in a world Merton Miller (1977) argues that in a world of differential personal taxes, (1) the of differential personal taxes, (1) the marginal personal tax disadvantage of debt marginal personal tax disadvantage of debt combined with (2) supply side adjustments combined with (2) supply side adjustments by firms will override the corporate tax by firms will override the corporate tax advantage of debt and drive market prices advantage of debt and drive market prices to an equilibrium implying leverage to an equilibrium implying leverage irrelevancy to any given firm.irrelevancy to any given firm.
Importantly, the existence of a unique Importantly, the existence of a unique interior optimum does not require the interior optimum does not require the introduction of bankruptcy, agency, or other introduction of bankruptcy, agency, or other leverage-related costs. On the other hand, leverage-related costs. On the other hand, with any of these leverage costs present with any of these leverage costs present each firm will also have a unique interior each firm will also have a unique interior optimum capital structure regardless of optimum capital structure regardless of whether non-debt shields are available.whether non-debt shields are available.
Most interestingly, our model predicts that Most interestingly, our model predicts that firms will select a level of debt which is firms will select a level of debt which is negatively related to the (relatively easily negatively related to the (relatively easily measured) level of available tax shield measured) level of available tax shield substitutes for debt such as depreciation substitutes for debt such as depreciation deductions or investment tax credits.deductions or investment tax credits.
Element of modelElement of model
Use a two-date state-preference modelUse a two-date state-preference model For firmFor firm - maximize its value- maximize its value - treat debt charge as deductible in - treat debt charge as deductible in calculating the corporate tax billcalculating the corporate tax bill - have deductible non-cash flow charge as - have deductible non-cash flow charge as well as tax creditswell as tax credits For investorsFor investors - select optimal portfolio according to their - select optimal portfolio according to their risk-preference and personal tax statusrisk-preference and personal tax status - personal tax code treats equity income - personal tax code treats equity income more favorably than debt incomemore favorably than debt income ( i.e. ) ( i.e. )
iPE
iPD 0
Aggregate demand for debt and Aggregate demand for debt and equity under differential personal equity under differential personal taxation taxation Define and as Define and as
individual i’s after-personal tax yields individual i’s after-personal tax yields on state s debt and equityon state s debt and equity
- If >If > holds state s debt over equityholds state s debt over equity- If =If = indifferent to holds either state s debt indifferent to holds either state s debt
or equity or equity - If <If < holds state s equity over debtholds state s equity over debt
SPD
iPD1
SPE
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SPD
iPD1
SPD
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SPD
iPD1
SPE
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SPE
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SPE
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Each of the following mutually Each of the following mutually exclusive and exhaustive personal tax exclusive and exhaustive personal tax bracketsbrackets
Bracket B.1:Bracket B.1: Bracket B.2:Bracket B.2: Bracket B.3:Bracket B.3: After-personal tax expected yield on After-personal tax expected yield on
debt and equitydebt and equity
ciPE
iPD 111
ciPE
iPD 111
ciPE
iPD 111
sP
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s
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cEP 1
Ddebt
FlowCash Debt
ExpectedTax Personal
Before ofPer Unit
Before PriceMarket
flowCash Debt Tax Personal BeforeExpect
DP
EP
Firm valuation under Firm valuation under differential personal taxation differential personal taxation Define the following variablesDefine the following variables X(s)X(s)≡≡ state s earning before interest and taxes state s earning before interest and taxes (be monotone increasing in s over the set of (be monotone increasing in s over the set of possible states [ 0 , ])possible states [ 0 , ]) B B ≡ ≡ face value of debt which is assumed fully face value of debt which is assumed fully deductible in calculating the corporate tax bill deductible in calculating the corporate tax bill (capital structure decision variable)(capital structure decision variable) △ △ ≡ ≡ corporate tax deduction resulting from non- corporate tax deduction resulting from non- cash charges such as accounting cash charges such as accounting depreciationdepreciation Γ Γ ≡ ≡ dollar value of tax creditsdollar value of tax credits ≡ ≡ statutory marginal corporate tax ratestatutory marginal corporate tax rate θ θ ≡ ≡ statutory maximum fraction of gross tax liability statutory maximum fraction of gross tax liability which can be shield by tax credits which can be shield by tax credits
c
s
State outcomeState outcome
00
B B
BB
BB
sD sE
sX s1
0,sfor
sX -B ss 21,sfor
BsXBsXBsXCC
ss 32,sfor
BsXBsXC Ss ,sfor
3
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3
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The current market value of firm The current market value of firm is V=D+E where D and E are is V=D+E where D and E are the current market valuations the current market valuations ( at prices { })( at prices { }) sPsP ED ,
dssPsPBV s
s cED
31
dssPsPs
s cED 3
211
dssPsPs
s ED 2
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See how alternative leverage See how alternative leverage decision affect firm value, decision affect firm value, calculate the marginal value of calculate the marginal value of debt financingdebt financing
Consider all investors are risk-Consider all investors are risk-neutral with homogeneous beliefneutral with homogeneous belief
dssPP
dssPP
dssPPBV
s
sED
s
scED
s
scED
2
1
3
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11
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Miller’s leverage Miller’s leverage irrelevancy theoremirrelevancy theorem
Given no corporate tax shield Given no corporate tax shield substitutes for debt, partial or substitutes for debt, partial or total loss of the marginal total loss of the marginal corporate tax shield benefit of corporate tax shield benefit of debt never occur.debt never occur.
dssPPBV s
scED
11
cEP 1
FlowCash Debt
ExpectedTax Personal
Before ofPer Unit
Before PriceMarket
flowCash Debt Tax Personal BeforeExpect
Sdebt
Q
Ddebt
Given the heterogeneous personal tax Given the heterogeneous personal tax code, the downward-sloping aggregate code, the downward-sloping aggregate debt demand curve must intersect the debt demand curve must intersect the aggregate supply curve in the perfectly aggregate supply curve in the perfectly elastic range at relative elastic range at relative prices . prices .
dssP
BV s
scPEPDPD
D1
1111
cED PP 1
Tax shield substitutes Tax shield substitutes for debt and interior for debt and interior optimum leverageoptimum leverage
Bfull Q
cEP 1
Ddebt
Sdebt
flowCash Debt Tax Personal BeforeExpect
FlowCash Debt
ExpectedTax Personal
Before ofPer Unit
Before PriceMarket
Deriving the supply curve (1)Deriving the supply curve (1)
No firms will supply any debtNo firms will supply any debt
cED PP 1
0 BV
Deriving the supply curve (2)Deriving the supply curve (2)
Perfect elastic sectionPerfect elastic section
cED PP 1
s allfor 0 BXBsXcc
00 XXc
full
B
00for 1 XB fullBBVcED PP
Deriving the supply curve (3)Deriving the supply curve (3)
No debt will be supplied at the No debt will be supplied at the relative prices.relative prices.
A higher price must be paidA higher price must be paid To induce a greater supply of debt, a To induce a greater supply of debt, a
higher unit price must be paid.higher unit price must be paid.
0XBBfull
0 BV
Deriving the supply curve (4)Deriving the supply curve (4)
This higher price is required to This higher price is required to compensate for the loss of compensate for the loss of corporate tax shield which will corporate tax shield which will occur on marginal units of debt occur on marginal units of debt in states of the world .in states of the world . ss 31
,
Optimum leverageOptimum leverage
011 3
3
2
*
PD
s
C
PD
D
s
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dssdssB
V PB
At the term in square brackets At the term in square brackets equals zero which says that the equals zero which says that the expected marginal corporate tax expected marginal corporate tax benefit is equated to the expected benefit is equated to the expected marginal personal tax disadvantage marginal personal tax disadvantage of debt at the optimumof debt at the optimum
B*
CB-CF effectCB-CF effect
CB provisions reduce the probability that a CB provisions reduce the probability that a corporate tax shield will be lost by allowing current corporate tax shield will be lost by allowing current tax losses to be applied immediately against several tax losses to be applied immediately against several previous years’ unsheltered taxable income.previous years’ unsheltered taxable income.
CF provisions reduce the probability that corporate CF provisions reduce the probability that corporate tax shield will be lost by allowing excess shields to tax shield will be lost by allowing excess shields to be applied against future taxable income for several be applied against future taxable income for several years.years.
The supply curve will be more elastic since firms will The supply curve will be more elastic since firms will require smaller price compensation to increase their require smaller price compensation to increase their debt supply because CB-CF provisions reduce the debt supply because CB-CF provisions reduce the expected loss of corporate tax shield.expected loss of corporate tax shield.
Bankruptcy costs and Bankruptcy costs and horse-and-rabbit stewhorse-and-rabbit stew
With positive default costs, each firm will still have a With positive default costs, each firm will still have a unique interior optimum leverage decision in market unique interior optimum leverage decision in market equilibriumequilibrium
Whether default costs are large or small, the Whether default costs are large or small, the market’s relative prices of debt and equity will adjust market’s relative prices of debt and equity will adjust so that the net tax advantage of debt is of the same so that the net tax advantage of debt is of the same order of magnitude as expected marginal default order of magnitude as expected marginal default costs.costs.
s
DCPEPD
PD
D
D
s
CED
s
sdss
B
Cdss
sdss
B
C
s
dssBV
PP
PPP
1
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0
0
1111
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CED PP 1 The higher debt price is The higher debt price is required in market equilibrium as required in market equilibrium as compensation for the expected compensation for the expected marginal costs of default.marginal costs of default.
In market equilibrium, each firm will In market equilibrium, each firm will have a unique interior optimum have a unique interior optimum leverage decision which equates the leverage decision which equates the present value of expect marginal net present value of expect marginal net tax advantage of debt to the present tax advantage of debt to the present value of expected marginal default value of expected marginal default costs.costs.
Testable hypotheses & Testable hypotheses & Empirical evidenceEmpirical evidence
H.1: The leverage decision is relevant to the H.1: The leverage decision is relevant to the individual firm in the sense that a pure change in individual firm in the sense that a pure change in debt (holding investment constant) will have a debt (holding investment constant) will have a valuation impact.valuation impact.
H.2: In equilibrium, relative market prices will imply H.2: In equilibrium, relative market prices will imply a net (corporate and personal) tax advantage to a net (corporate and personal) tax advantage to corporate debt financing – i.e., the implied marginal corporate debt financing – i.e., the implied marginal personal tax rates will satisfy or equivalently,personal tax rates will satisfy or equivalently,
H.3: H.3: Ceteris paribusCeteris paribus, decreases in allow able , decreases in allow able investment related tax shields (e.g., depreciation investment related tax shields (e.g., depreciation deductions or investment tax credits) due to deductions or investment tax credits) due to changes in the corporate tax code or due to changes in the corporate tax code or due to changes in inflation which reduce the real value of changes in inflation which reduce the real value of tax shields ill increase the amount of debt that firms tax shields ill increase the amount of debt that firms employ. In cross-sectional analysis, firms with lower employ. In cross-sectional analysis, firms with lower investment related tax shields (holding before-tax investment related tax shields (holding before-tax earnings constant) will employ greater debt in their earnings constant) will employ greater debt in their capital structures.capital structures.
H.4: H.4: Ceteris paribusCeteris paribus, decreases in firms’ marginal , decreases in firms’ marginal bankruptcy costs will increase the use of debt bankruptcy costs will increase the use of debt financing. Cross-sectionally, firms subject to greater financing. Cross-sectionally, firms subject to greater marginal bankruptcy costs will employ less debt.marginal bankruptcy costs will employ less debt.
H.5: H.5: Ceteris paribusCeteris paribus, as the corporate tax rate is , as the corporate tax rate is raised, firms will substitute debt for equity financing. raised, firms will substitute debt for equity financing. Cross-sectionally, firms subject to lower corporate Cross-sectionally, firms subject to lower corporate tax rates will employ less debt in their capital tax rates will employ less debt in their capital structures (holding earnings constant).structures (holding earnings constant).
SummarySummary
