Tax arbitrage restrictions and financial leverage clienteles

Journal of Banking and Finance 13 (1989) 831-838. North-Holland

TAX ARBITRAGE RESTRKTIONS AND FINANCIAL LEVE CLIENTELES Eli TALMOR* To1Aviv University,

Tel Aviv, Israel Utiversity of Cd~omia, Irvine, CA 92717, USA

Received May 1988,final version receivedNovember 1988 This paper argues that while total short sale constraints are o&n introduced to rule out tax

arbitrage, such constraints are both unrealistic and conceptually problem&c. Instead, milder constraints are advocated, which prevent tax arbitrage while still allow short positions. It is demonstratedthat a model with these constraintsemployed can support bond pricing as in the Miller equilibrium,although it leads to a richer set of tax clienteles.

1. Inhrodpction

The issue of differential taxation across securities is a perplexing topic which has received increased attention in financial theory. Of particular interest to both policy makers and academic scholars in finance is the distinction between capital gains taxation and ordinary income taxation. This bears fundamental implications on asset pricing and investors’ clienteles of both dividend policy and capital structure.’ A natural concern in these models is the ability of agents to sell securities short. It is well known that when financial securities are taxed differentially, and at least some investors are taxed linearly (e.g. tax-exempt), there could be no-equilibrium prices, unless there are restrictions on trade; otherwise, for any set of prices, there could be infinite gains to trade. To rule out tax arbitrage possibilities, the usual formulation of capital market equilibrium in the literature restricts individuals from short selling securities [e.g., Taggart (1980) and Dybvig and Ross (1986)]. Not only is there no total ban on short sales in actual practice, but such a ban also creates a conceptual problem. Consider individuals with low income in the present and a substantially higher future income. These individuals would *I would like to thank Simon Benninga, Lemma Senbet, Herbert Shapiro and two anonymous

refereesfor helpfulcomments. ‘Recent papers that deal with differentialtaxation and equilibrium prices are Dybvig and Ross (1986) and Dammon and Green (1987). Recent studies on financial leveragetax clienteles are Sarig and Scott ( 1985)and Aivazianand Callen ( 1987). 03784266/89/$3.50 @ 1989,ElsevierScience PublishersB.V. (North-Holland)

832

E. T&w,

Tax arbitrage restrictions

typically show a propensity to borrow, not necessarily in order to exploit tax

arbitrage, but out of a fundamental desire to smooth consumption over time. For example, the short sale restrictions imposed in the Miller (1977) equilibrium model to prevent tax arbitrage also forbid these investors from borrowing, and so force their marginal rate of time substitution from consumption to deviate from any market interest rate. Most of the extensions of the Miller model similarly require no arbitrage conditions and thus are subject to the same difftculty.2 The obvious question that arises is one of finding conditions, if they exist, under which it is possible to relax the no borrowing constraint. In the formulation below, we impose restrictions that rule out tax arbitrage while still allow short positions. To facilitate the analysis we concentrate on the Miller model and on financial leverage clienteles. However, the methodology presented may be useful also for dealing with tax arbitrage restrictions in a broader class of equilibrium models.

We consider a two-date certainty world in which individuals maximize their utility of consumption subject to budget equations which govern that consumption, investment and tax payments balance income from all sources.3 Individual i receives a labor (or endowed) income of Yli at Date 1 and Y2iat Date 2? In addition, each individual is endowed at Date 1 with shares in each firm. Since ‘under certainty shares in all firms are perfect substitutes, we will denote by ditthe initial ownership shares of individual i in total corporate stocks. On the uses side, each individual i consumes C,i at Date 1 and can invest in (or borrow) financial securities. These include stocks, corporate bonds and municipal bonds. We retain the Miiler assumption that return on equity is tax-exempt.’ Thus, shares and municipal bonds are perfect substitutes and should yield the same return. We will denote the total value of shares S and the value of municipal bonds AN. 2Extensions of the Miller model that require short sales restrictions include, among others, Kim, Lewellen and McConnell ( 1979), DeAngelo and Masulis ( 198Oa, 198Ob),Bradley, Jarrell and Kim (1984), Zechner and Swoboda (1986), Barnea, Haugen and Talmor (1987) and Ravid and Talmor ( 1988). 3As pointed o ut by DeAngelo-Masulis (198Ob)and Taggart (1980), the Miller case of certainty also applies under uncertainty, provided that markets are truly complete so that both taxable and tax-exempt state contingent securities can be created (i.e., ‘double spanning’). For further analysis see Dammon (1988). 4To the extent possible, the basic set-up of the model and most of the notation follow Taggart (198Oj. ‘This assumption is maintained for expositional convenience. The effective U.S. tax rate on capital gains can be substantially less than the statutory tax rate due to the tax timing option analyzed by Constantinides (1983). Also, the tax code allows a write-up in the base at time stocks are inherited making the capital gains tax on these stocks zero. For a thorough discussion of the Miller assumptions under the U.S. TRA of 1986, see Benninga and Talmor (1988) and Scholes and Wolfson (1989).

E. Talmor, Tax arbitrage restrictions

833

Corporations invest an amount I in Date 1 and finance it with bonds and equity. At the end of the period, Date 2, corporations generate an operational income taxed at the rate tc on their income, and pay back both their debt principal, B, and the interest charges, tB. Interest payments and the real investment, I, are tax deductible for the corporation at Date 2! Each investor is taxed on his interest income at a fixed personal rate tpi, which is heterogeneous across investors. We will denote the fraction of corporate bonds purchased by investor i as pi. Similarly, a, will denote the fraction of stocks and municipal bonds held by the investor over the period. Lastly, but most importantly for the current purpose, we will impose the no tax-arbitrage constraint @i>=O. This constraint aims to capture the essence of the tax regulation which generally disallows personal interest expenses to be tax deductible. We thus permit individuals to either borrow (and to deduct interest) or to short sell equity, provided that no long position is maintained concurrently in the other type of security. [We essentially disallow the following two situations: (ai < 0 n fli > 0) u (ai > 0 n fii < O)]. Stated another way, individuals are permitted to borrow and to deduct interest, as long as the proceeds are used for current consumption, and not for the purchase of financial securities.’ Suppressing subscript i for notational convenience, the optimization problem each investor faces is: Max U(C1, C,)

*

a4

subject to C1 +BB+a(S+M)=

apz0

& btZ(S+B-I)

(1)

(3)

where V(e) is the utility of consumption, and r and r. are the rates of return on taxable and tax-exempt bonds, respectively. Since equity and tax-exempt bonds are perfect substitutes in the stylized environment of the model, they should have the same return. Thus

6The particuIar depreciation tax schedule allowed is irrelevant in the current context, as it affects only the marginal rate of return in production and consequent!y the magnitude of corporate investment. ‘For example, interest on home mortgages may be deductible, as in the U.S.

E. Tabnor, Tax arbitrage restrictions

834

and so eq. (2) simplifies to Gz=Yz+0@+M)(l

+ro)+j?B(l +r(l-tp)).

I

(2 )

The Kuhn-Tucker conditions for an optimal portfolio are dL -= au

-u,(S+M)+u,(S+M)(l

dL -= -trlB+u,B(l alJ

+@+A/?=0

+r(l -t,))+Aa=O

(5a5J

cw

dL

-=a~~0 an AsO

6W

Ra/?=O

152)

where ul = XJfX, and u2 = dUldC2. Analyzing conditions (5~) through (se), there are several alternative cases which each applies to a different clientele of investors. We will investigate each case in turn

0i

A=O.

Together (Sa) and (Sb) yield that y,,

= 1 +r(l

-t,),

which holds for investors for whom t,+Yo.

Y

[Condition (6a) also applies to the trivial case a = fl=O]. (

ii) a=O, /bO. ii,>O. Substituting in (5a) and (Sb) implies that

(6a )

E. Talmor, Tax arbitrage restrictions

835

!-k+r(l--t,)>l+r,, Ul which holds for investors at personal tax brackets t,
F

(iii) of=O, /?O. The inequality in this case is reversed U’=l+r(l-t,)
(iv) fl=O, a>O, ;1>0. For this case, it is obtained that U’=l+@+r(l-tJ, u2

and so t,>l--‘?

’ Y

(v)

jY=Og ae0,

il>O.

Comparing (Sa) to (5b) implies Q*,,
which holds for investors at personal tax rates t,
(6C 1

836

E. Talmor, Tax arbitrage restrictions

Group (i) includes investors that are indifferent in equilibrium between the various securities. Each investor in this group will purchase or borrow any of these securities depending on his consumption needs. Group (ii) comprises investors that wish tcr save and prefer investing in taxable securities. Investors in Group (iii) wish to increase their current consumption and are at a relatively high tax bracket. They will prefer, therefore, borrowing over selling equity short. Like Group (iii), investors in Group (iv) are also at a relatively high tax bracket, but they prefer saving over borrowing. For tax purposes they will invest in equity (or tax-exempt bonds) and not in taxable debt. Finally, investors in Group (v) wish to have more funds at the present time, and because of tax considerations, they prefer selling equity short rather than borrowing. 3+ Equilibrium We shall first inspect the preference of the initial shareholders to a change in the financial leverage of each company. In particular, it is important to verify that the restrictions on borrowing at the personal level do not impair shareholders’ unanimity with respect to corporate borrowing. Using a subscript j to denote variables of company j, then Si and Bj are the total values of equity and debt of that company, and IIZ~ is the initial fraction of firm j’s shares owned by the investor. Differentiating the utility of the investor with respect to Bj using (l), (2’) and the envelope theorem, yields

(7) Denoting *I =ul - u2(.l+ rO) and e2 = u1 - u2(1+ r( 1 - Q), will show that both the terms $Iar and e2b in eq. (7) are equal to zero for all groups of investors. For Group (i) we substitute A=0 in eqs. (Sa) and (Sb). Differentiating both (5a) and (5b) with respect to Bj produces *I =e2 =O. kor Groups (ii) and (iii), oc=0 and so the first term of eq. (7) is clearly zero. Substituting oc=O in eq. (5b) and differentiating with respect to Bj yields ti2 =O. Finally, for Groups (iv) and (v), /I = 0. Employing a similar procedure yields *I = 0. Therefore, at a portfolio equilibrium, the first two terms in (7) are zero, implying that regardless of the group to which each initial shareholder belongs, his preference to changes in I$ depends entirely on the last term. This ensures that the restrictions on consumer trading do not introduce a tension among shareholders regarding corporate financial leverage, and so do not impair the unanimity condition essential for value maximization.

E. Talmor, Tax iarbitragerestrictions

837

To obtain the value maximizing corporate capital structtirre, we totally differentiate eq. (4) and substitute it in eq* (7). This leads to dU/dBj= ul$[rO -r( II- Q]/( 1+ Q,). Since the bracketed term is uniform across -alI firms, corporate supply adjustment drives it to zero. Hence in equilibrium, taxable interest is grossed up by the corporate tax rate: r0

r=l_t,’

(8)

which is the Miller equilibrium result. Utilizing (8) enables us to identify the five clienteles according to their personal tax brackets. Substituting (8) in (6a) yields that investors belong to group (i) if tP=tr. Clearly, constraint (5~) is not binding since no arbitrage opportunities are available for this group. For groups (ii) and (v), it is obtained that fp< tc. Thus they comprise investors below the corporate tax rate. Investors with a propensity to save will buy corporate debt (ii), while those with a propensity to consume at Date 1 more than their available funds will sell equity short, and so belong to (v). Finally, for groups (iii) and (iv), t,> t,. Depending on their desired consumption pattern, individuals in high personal tax brackets (above the tax rate t, embedded in the securities price differentials) will either invest in equity (Group (iv)), or borrow (i.e., short sell taxable debt) and will belong . .. then to Group ( 111) . 4. Conchsion This paper maintains that the total short sales constraints used in the literature are both conceptually problematic and do not accurately describe the actual practice. We offer instead milder constraints that allow individuals for short positions provided that the proceeds from the short sales are used for current consumption, and not to establish a long position in financial assets with a differential tax status. Hence, we prevent tax arbitrage while we explicitly permit borrowing. It is demonstrated that a model with these constraints employed can support bond pricing as in the Miller equilibrium, although the formation of tax clienteles is more intricate. The methodology presented may be useful for other cases that require short sales restrictions, such as other effects of taxation on asset pricing [e.g., Dybvig and Ross (1986)], normative portfolio theory and tax timing options. Refemces Aivazian, V.A. and J.L. CalHen, 1987, Miller’s irrelevance mechanism: A note, Journal of Finance 42, 169-180.

838

E. Talmor, Tax arbitrage restrictions

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