0NDERZOEKSRAPPORT NR. 8603 TAXES, DEBT AND FINANCIAL INTERMEDIARIES BY C. VAN HULLE Wettelijk Depot : D/1986/2376/4
TAXES, DEBT AND FINANCIAL INTERMEDIARIES Muh lending and borrowing is indiret : finanial intermediaries fulfill the task of olleting surpluses hanelling them to eonomi agents in need of redit. The reason why banks instead of finanial markets are attributed this task is that they (i.e. banks) save on osts. Taxes are one important lass of suh osts. In fat, as soon as there exist differenes in tax treatment between individuals and firms the intervention of a finanial institution may be very useful. Those differenes in taxes, just as in the ase of other ompanies, affet a bank's optimal apital struture, and as it turns out also its profitability (i.e. return on equity). This paper fouses on finanial intermediaries as vehiles for minimizing tax payments. Simultaneously it is seen how the intervention of suh institutions affet the optimal apital struture of non finanial ompanies and M. Miller's equilibrium from "Debt and Taxes". At the same time some relationships between the tax struture, bank profitability and optimal debt/equity ratio emerge. 1. Tax struture, bank profitability and debt struture the simplest ase 1. 1. The mode 1 Consider a simple ~period world in steady state : individuals have surplus funds whih they may invest in firms through equity or perpetual debt instruments, diretly or indiretly through finanial intermediaries. Any industrial ompany has invested in a projet whih perpetually generates some stohasti return X in every period. Markets are omplete and ompetitive and everybody has the same expetations. It is assumed that every period both ompanies (inluding finanial institutions) and individuals are taxed on their inome at the respetive rates r and r (for the moment r is assumed p p 1. The expressions "bank" and "finanial intermediary" or "finanial firm" are used interhangeably.
2 equal among individuals). Also suppose that every period there are some monitoring osts assoiated with holding finanial instruments ; assume that these osts are proportional and amount to per unit of equity e. and d per unit of debt for all market partiipants (i.e. also for finanial intermediaries). Suppose that through government regulation the individuals' monitoring osts on bank debt and equity is very low, that in fat, for pratial purposes one may set it equal to zero. Assume further that banks are not allowed to invest in equity and that the orporate tax treatment of holding ompanies is suh that no savings an be realised by indiret equity holding. Thus banks' period inome onsist of interest payments on their lending to orporations. Further assume that e is lower than d' in partiular that it is equal to d(l-r). Further assume for simpliity that, ontrary to interest inome, inome from equity goes'untaxed for individuals. Also aept that, ontrary to orporations, individuals annot subtrat monitoring osts from taxable inome (in most real world tax odes individuals annot or at the most only partially subtrat the effort and money spend on Lnvestigating and following up the quality of loans). Suppose that after personal taxes and osts, individuals want a risk free rate of return amounting minimally to ~ per period ; this rate remains onstant over time. For the moment assume that the monitoring effort allows debt to remain without bankrupty risk. Preeding assumptions are many. Nevertheless only the highth of r relative to r and the differene in the way in whih orporate and personal tax p treat monitoring osts and equity inome basially drive the subsequent findings. The reason for onstruting the model this way is that it allows a "ontrolled experiment" in whih the tax effets get perfetly separated out from other onsiderations (returns to sale in monitoring osts by finanial firms, ageny problems... ). 1.2.!~}!~at!~~~-~E_!~~E! E_~~b!_!~~!~i~~~b~-!~~-~~~-E~E~ ~~±-!~~-E~!~ The purpose of this subsetion is to show to what extend differenes in orporate and personal tax rules fosters the use of intermediaries' servies and how the existene of these firms affets finaning deisions. To that end onsider the total return on a non-finanial firm's assets aruing to investors with diret orporate borrowing at the end of any period:
3 1 (X- R D) (1-r.) - (V-D) (1-r ) + R D(l-r ) - D. F d F p d (1) with X a realisation of the ompany's earnings before interest and taxes in the period RF the riskfree orporate borrowing rate D the market value of the firm's debt V : the total market value of the firm When lending ~s hanneled through a bank, total return equals : with the riskfree rate on bank deposits ; DB the market value of the bank's debt At first sight one would undoubtedly expet that the optimal apital struture of industrial firms depends on the highth of r p relative to r and hene that the existene of a finanial firm would depend upon hoie, viz. when r < r no banking firm, and when possibly indiret lending. p this debt-equity one would expet full equity finaning and hene r < r one would expet all debt finaning anq p It turns out that the existene of the bank does not really depend on whether or not the rat~o \r /r ) ~s. p larger or smaller than one. However banking profits and apital struture prove to be dramatially affeted by this ratio, in a way even more so than the optimal debt/equity deision for industrial orporations. To see this, note that the differene in return between diret and indiret lending an be written as : (3) Clearly, indiret lending is preferred if the R.H.S. of (3) is positive and the more so as the differene gets larger. In the ase rp < r this goal is ahieved by minimising (RFD- rfdb) or squeezing bank profits. In fat, the optimal solution is ahieved when bank 1. (V-D) d (1-r ) represents the monitoring osts relative to equity..
4 profits are zero ; then, given that everybody wants to earn a rate of return of at least ~, the fores of ompetition would be responsible for the fat that finanial institutions would be unable to attrat equity suh that neessarily D =DB. Consequently, given a monitoring outlay of d per unit, the optimal rate on bank deposits would be rf = (~- d) whih, in ompetition, would equal Taking the preeding fats into aount, the differential return YB- YNB would then redue to Hene if some orporate borrowing ours, ompetition would enqure that it would take plae through the intermediation of a bank paying (~-d) on its deposits. Therefore with a debt poliy D, the following is left from the return on an industrial projet = X ( 1-r ) -r (RF-d) D (r -r ) - d(l-r )V. p With a rate. flows is disounting E(X)(l-r.), the total present value of these v E (X) (1-r) ] = + D(r.-r) [ : p 1 (4) with E(X) any period's expeted earnings before interest and taxes. Sine rt < rp, equation (4) implies that the optimal poliy for the industrial orporation is to debt finane as muh as possible. When rp > r:t, the R.H. S. of (3) is maximised when RFD- rfdb is as large as possible. This learly ours when rf=o, whih implies that, as the minimal after personal tax return on a riskfree asset is ~. banks will be fully equity finaned and profitable. Consequently in ompetition one would find that yielding ~ as an after ost and after tax return on bank equity.
5 Sine ~n that ase intermediation will our if some orporations borrow. To find out about the latter, onsider again any period's after-osts-and taxes-return on an industrial projet, given debt poliy D and optimal bank behavior With a rate of v = X ( 1-r ) - ( 1-r. ) V d Cl: E(X) (1-r. ) disounting E(X)(l-r ), this would result in a market value (5) whih is learly independent of D. Thus, if r > r the intermediation of finanial orporations plaes a p eiling r on the effetive personal tax rate paid on interest inome and the hoie of debt-equity ratio of any nonbank ompany is irrelevant for valuation. The simplest version of the model disussed until now yields the following main onlusions : - if rp < r' optimal orporate poliy for industrial firms is full debt finaning ; when d > 0 one may expet lending through the intermediation of finanial institutions, the latter having the tendeny to be highly levered and show low profitability on equity sine in suh a world, the borrowing rate for non-finanial firms is equal to ~ = l-r + d, this p borrowing rate an be redued by dereasing r. finally yields on bank deposits are likely to be high ( r =_'IT_ ) and just as the borrowing rate, F 1-r p have the tendeny to vary with hanges in the personal tax rate ; p ' 'IT
6 if r p ~ r the hoie of debt equity ratio for non finanial ompanies is irrelevant when borrowing operations involve a finanial intermediary ; then banks tend to have a high level of equity finaning and good profitability ; yields on bank deposits are likely to be low and sine the ~ borrowing rate for firms is ~ = l r + d, RF an be redued by dereasing the orporate tax rate. 2. Equilibrium with a ontinuous sale of personal tax rates Given the preeding analysis, pereption of the a sale of personal tax rates between say 0 % and equilibrium situation with 100 %, is straightforward. From equation (4) it follows that firms will lever up with loans banks provide as long as the personal tax rate of the marginal group of deposit holders rm is below r p Finanial institutions from their side attrat the funds supporting the loans from onseutively higher and higher tax paying groups of individuals thereby inreasing the deposit rate from ~ to ~ m 1-r p All this time banks ontinue to be fully debt finaned. m ontinues at least until r = r. p The proess learly At this point the finaning deision for both finanial and non-finanial ompanies is irrelevant. In partiular banks pay equity and harge ~ = l~r + d on loans. ~ ---- on deposits and 1-r Could the proess of issuane of additional debt go on beyond this point, i.e. have rm > r? p The analysis of the previous subsetion shows the answer is yes : bank intermediation plaes an upper eiling r on the effetive personal tax rate. Speifially, as the proess of inreasing orporate borrowing ontinues, individuals with r. > r ontribute to this type of finaning by purhasing p bank equity. Simultaneously the orporate borrowing rate stays put at
7. 1T R -F = -- 1-r + d and the rate on bank deposits at 1T rf = 1-r The finaning deision for any one industrial firm is irrelevant, and assuming smallness of any finanial intermediary, this holds true for any one bank also. On the maro-level the equilibrium is as depited below Interest rates 1T -1-- + d -r --... " r------ 0 Quantity borrowing nonfin. firms Interest rates 1T 1-r 1T Quantity bank depos
8 In both graphs the horizontal line through (l~r + d) respetively (l~r ) depits the orporate demand for debt instruments. inreasing urve through debt instruments. Also in both ases the n+d, respetively n, represents demand for However, ontrary to Hiller's finding in [3], no unique optimal quantity of outstanding debt on the maro-level exists. In partiular, any quantity of debt taken up by non-finanial firms beyond the point XNB ould do as an equilibrium, and this notwithstanding the X fat that the total quantity of bank deposits is uniquely determined at XB. The only (and obvious) ondition whih must hold is that (XNB- X~) (~B - X~) represents bank equity. ~ 0 where 3. Tax struture and risky debt It is well known that as long as there are no leverage-related osts (i.e. loss depreiation tax shield, bankrupty osts, ageny problems..), riskyness of debt does not affet any of the Miller findings in [3] (e.g. see Constantinides [1], S. Ross [4]). Clearly the same holds true for the equilibrium of the previous setion. However, as soon as one allows depreiation tax shields, an equilibrium with the marginal group of debtholders having may obtain. In that ase the tax advantage of further debt finaning must be traded off against the hane of loosing some of the depreiation tax shield and an internal optimal leverage deision may exist. This optimal leverage position is firm speifi and depends on the variability of EBIT (i.e. earnings before interest and taxes) and the amount of depreiation allowanes (see De Angelo and Masulis [ 2]). In that ase, given the same expeted period's return on ompany investment, firms with a ertain EBIT have an advantage over those whih have an inome stream with possible large downward deviation from expeted value. m The reason is of ourse that if no unertainty surrounds EBIT and sine r <r, p this type of ompany an maintain high debt ratios and apture a large amountof
9 D(r - rm) as a tax subsidy without any hane of loosing the depreiation p tax shield. 1 1. To see that variability of returns negatively affets expeted returns net of osts and taxes, onsider the following two firms - at the end of any period EBIT of firm a equals either 140 or 60, with a at 50-50 hane ; -firm b is ertain to have ABITb= 100. Clearly E(EBITb) = 100 = 1/2 140 + 1/2 60 = E (EBITa). Any period both firms an maximally subtrat SO in depreiation expenses and unused tax shields annot be transferred to future periods. Assume in equilibrium r = 0.5 and rp = 0.3 ; for the sake of simpliity e = d = 0. Evidently, the optimal poliy for firm b is to pay 50 in interest expense eah period suh that after taxes the following total return remains : Yb (EBIT,D) = (100-50 - 50)(1-0. 5) + 50 + 50(1-0.,3) = 85 Denoting by R the interest rate on its debt, debt poliy D allows firm a to generate an after tax total return of : Y (EBIT=l40,D) = (140- SO- RD) (1-0.5) +50 + RD(l-0.3) a = 95 + 0.2 RD = (140 - RD) + RD(l-0.3) = 140-0.3 RD = 140(1- o. 3) = 98 if RD,.;; 90 if 90 < RD,.;; 140 if RD > 140 Ya(EBIT=O,D) Summarizing (60-50-RD)(l-0.5) +50+ RD(l-0.3) 55 + 0.2 RD = (60- RD) + RD(l- 0. 3) = 60-0.3 RD 60(1- o. 3) = 42 for firm a : if RD,.;; 10 if 10 < RD,.;; 60 if RD > 60. 1 Return ~ EBIT =140 EBIT =60 E(Ya(EBIT,D)) Debt level a a RD.;;; 10 95 + 0.2 RD 55 + 0.2 RD 75 + 0.2 RD 10 < RD.;;; 60 95 + 0.2 RD 60-0.3 RD 77.s - 0.05 RD 60 < RD.;;; 80 95 + 0.2 RD 42 68.5 + 0.1 RD 90 < RD.;;; 140 140-0.3 RD 42 91-0.15 RD 140 < RD 98 42 70
ld footnote 1 ontinued. The optimal debt level is the one suh that max {75 + 0.2 RD, 77.5-0.05 RD, 68.5 + 0.1 RD, 91-0.15 RD, 70} RD given the preeding table's bounds on RD. The maxlmlslng RD~ = 90 and the maximal value of expeted total returns, E(Ya(EBIT,D~))=77.5. Hene, given the same expeted EBIT, the total expeted return on firm's b stoks and bonds is higher (i.e. E(Yb(EBIT,D~)) = 85) than a's. Further supposing that the orrelation of b's EBIT relative to other stoks is suh that it warrants no negative risk premium, learly Va < Vb. Herte under the example's irumstanes (rm <r, untransferrable tax shields implying no ash outlays), absene of varirbility in orporate returns is a thing of value.
11 As in that ase total risk affets valuation (see footnote 1, page 9), the best poliy for the bank, if it has depreiation allowanes, is to form a riskfree debt portfolio by taking up only riskfree loans and/or suffiiently diversify risks. 1 Likewise non finanial firms, banks have an optimal debt-equity struture whih obeys the rule : if depreiation allowanes relative to total assets are small and EBIT does not show muh variability, a high level of leverage is optimal. On a maro-level, if rm < r, ontrary to the ase disussed in setion 2, p the total amount of borrowing by non-finanial firms is uniquely determined, the reason being that with an optimal debt-equity struture of banks, the tota 1 amount o f b an k.. f' d 2 equ~ty ~s ~xe 1. When the loan portfolio is suffiiently diversified and risks unorrelated E( L: R.D.) = L: R.D. with R. a realisation of the risk adjusted borrowing J J j J J J rate harged to ompany j. 2. If banks onstrut a riskfree debt portfolio the graphial representation of the equilibrium would be as follows : Returns Returns -... --...,.... -.....,...-..,._... 'If total quantity of non-finanial orporate borrowing x" 6 quantity of bank deposits
12 4. Conlusions Finanial intermediaries typially are highly levered and often have debtequity ratios lose to the minimal regulatory requirements. This ould be onsistent with a world in whih the personal tax rate of the marginal investor in taxable debt instruments is below the orporate tax rate. In suh a setting, return on bank equity is squeezed and finanial institutions have the natural tendeny to be highly levered. In that ase there also is some advantage to "limited riskiness" of a bank's loan portfolio. The fat that firms an subtrat loan-evaluation and monitoring osts from taxable inome, whereas individuals an't (or only to a limited extend) fosters the use of finanial intermediaries. The model would therefore predit that borrowers for whom lending entails little evaluation- and monitoring expenses, have the tendeny to diretly plae their debt in the finanial markets. Furthermore, even in the ase that the marginal debt holders' personal tax rate on interest inome is above the orporate tax rate, orporate borrowing may still our through the intermediation of banks ; then finanial struture of both finanial institutions and non-bank firms and ompany market value remain independent.
13 Bibliography G. Constantinides, Disussion, Journal of Finane, July 1985, 657-658 H. DeAngelo and R. Masulis, Optimal Capital Struture Under Corporate Taxation, Journal of Finanial Eonomis, Marh 1980, 5-29. M. Miller, Debt and Taxes, Journal of Finane, May 1977, 261-276. S. Ross, Debt and Taxes and Unertainty, Journal of Finane, July 1985, 637-657.