Optimal dividend policy, debt policy and the level of investment within a multi-period DCF framework

Pacific-Basin Finance Journal 19 (2011) 21–40

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Pacific-Basin Finance Journal j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p a c f i n

Optimal dividend policy, debt policy and the level of investment within a multi-period DCF framework Martin Lally School of Economics and Finance, Victoria University of Wellington, PO Box 600, Wellington, New Zealand

a r t i c l e

i n f o

Article history: Received 7 January 2010 Accepted 13 August 2010 Available online 21 August 2010 JEL classification: G31 G32 G35 Keywords: Optimal dividend policy Optimal debt policy

a b s t r a c t This paper simultaneously analyses optimal dividend, debt and investment policy within a conventional multi-period DCF framework, and takes account of differential personal taxation over both investors and types of income, the effect of dividends and interest on the level of share issues and hence share issue costs, and the effect of dividends and interest on the level of internally-financed investment. Application of the model to three distinct tax regimes reveals that the value benefit from debt is small at best whilst the value benefit from dividends is substantial even in a regime without dividend imputation. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Consideration of optimal dividend policy and capital structure commences with Modigliani and Miller (1958, 1961, 1963), who show (separately) that debt is desirable and that dividends are irrelevant to a firm's value if (inter alia) all forms of personal income are equally taxed. DeAngelo and Masulis (1980a) extend this analysis to recognise personal tax rates that vary over both investors and sources of income; they also simultaneously consider optimal debt policy, which is desirable because dividends and interest are alternative means for disbursing internally-generated cash flow to investors. They conclude that debt is irrelevant but dividends may be relevant to a firm's value. Fung and Theobald (1984) extend this analysis to dividend imputation systems. However, both of the latter two papers treat “internally-financed” investment (i.e., that which is internally-financed and would not otherwise have been undertaken) as having zero NPV, and they ignore the implications of dividends for the level of share issues with their associated issue costs. In addition, the analysis in both papers is single rather than multi-period, and invokes a state-preference approach rather than a risk-adjusted discount rate. Whilst these last two features are useful for the purpose of assessing issues at an abstract level, the first of them is considerably less realistic, and the second considerably more difficult to implement, than the multi-period DCF framework that is generally employed for capital budgeting decisions. E-mail address: [email protected]. 0927-538X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.pacfin.2010.08.002

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Masulis and Trueman (1988) also recognise personal tax rates differing over both investors and types of income and, unlike the previous papers, recognise that “internally-financed” investment may not have zero NPV. Boyle (1996) extends this analysis to tax regimes with dividend imputation. However, the analysis in both papers does not simultaneously consider debt policy nor does it take account of the implications of dividends for the level of share issues with their associated issue costs. In addition, as with DeAngelo and Masulis (1980a) and Fung and Theobald (1984), the analysis is single rather than multi-period, and invokes a state-preference approach rather than a risk-adjusted discount rate. In a related paper focusing upon the tax benefits of debt and recognising that the corporate tax deduction on interest is not always usable or immediately usable, Graham (2000) concludes that significant levels of debt appear to be optimal for tax reasons and add significantly to firm value. However, he does not simultaneously optimise dividend policy and he assumes that dividends are paid in the conventional form rather than in the tax-preferred form of share repurchases (ibid, p. 1912). Green and Hollifield (2003) overcome many of the limitations in this earlier work. In particular, they simultaneously optimise debt and dividend policy for a given level of “externally-financed” investment (investment that is viable even if it is externally-financed), they recognise differential personal taxation over different types of income (but not investors), they recognise that “internally-financed” investment may not have zero NPV, their model is of the multi-period DCF form, and they recognise the bankruptcy costs arising from debt.1 Furthermore, their model dynamically accounts for investors' exercise of the deferral option relating to the payment of capital gains tax and also dynamically accounts for the firm's exercise of the bankruptcy option (with associated bankruptcy costs). However these last two features of the model are inconsistent with the conventional DCF framework that is generally employed for evaluating “externallyfinanced” investment projects, in which bankruptcy costs are recognised ex-ante through the cost of debt, and there is typically no allowance for differential taxation of interest, dividends and capital gains, let alone allowance for the deferral option in respect of capital gains tax.2 The use of one model of firm value for the purposes of optimising debt and dividend policy (and therefore the level of “internally-financed” investment), and a different model for optimising the level of “externally-financed” investment is unsatisfactory, because it effectively evaluates two types of investment using different methodologies and because the output from the first optimisation exercise ought to be incorporated into the second one. In view of these points, this paper seeks to develop a valuation model for the purposes of simultaneously optimising the level of debt, the level and type of dividends, and the level of “externally-financed” investment. The model must recognise significant real-world features that are relevant to optimising each of these policies and must also be readily amenable to implementation. The essential features of the model are as follows. Firstly, consistent with standard practice in evaluating investment projects, the model is of the multi-period DCF form with a risk-adjusted discount rate of the WACC form, and therefore allows for bankruptcy costs exante through the cost of debt.3 Secondly, consistent with the importance of personal taxes to optimal debt and 1 “Externally-financed” investment is that which is justified even if externally financed but this does not necessarily imply that it is actually externally-financed, i.e., it might be partly or wholly financed from internally-generated cash flows. To illustrate the importance of the distinction between “externally” and “internally” financed investment, suppose that dividends in any form were very highly taxed and capital gains were tax free. In this event, it might be desirable to retain internally generated cash flows and invest them rather than pay them as dividends or interest even if the NPV of the investments were significantly negative in the event of these investments being externally-financed. If such investments had a positive (negative) NPV in the event of being externally-financed, they would be called “externally (“internally”) financed” investment. 2 The failure to recognise differential taxation of interest, dividends and capital gains is implicit in the typical use of the standard form of the CAPM (Sharpe, 1964; Lintner, 1965; Mossin, 1966) for determining the cost of equity. 3 There are both pros and cons from this approach. The cost of debt comprises the risk free rate and the debt risk premium, and the latter comprises compensation for expected default losses, (systematic) risk associated with default risk and the inferior liquidity of corporate bonds relative to government bonds. Also, default losses arise from both bankruptcy costs and the default option possessed by equity holders. Since this default option is not a cost borne by capital suppliers in aggregate but merely a transfer between equity and debt holders, then the (conventional) approach to bankruptcy costs that is adopted here effectively overstates WACC. However, direct approaches to the issue of bankruptcy costs are also problematic. For example, Almeida and Philippon (2007) treat bankruptcy costs as a cost C that arises upon default. However, some bankruptcy costs are incurred by (highly-levered) firms even if they never default, in the form of customers, employees, etc. who avoid the firm or require compensation through lower prices, higher wages, etc. Furthermore, Almeida and Philippon's estimate of C is that of Andrade and Kaplan (1998), which is based upon a sample of firms experiencing bankruptcy and in which all of the decline in value from the time at which a highly-levered transaction was initiated until resolution of the bankruptcy is ascribed to bankruptcy costs rather than some combination of this and economic shocks. Thus, as noted by Andrade and Kaplan (ibid, p. 1487), their estimates of C are upper bounds.

M. Lally / Pacific-Basin Finance Journal 19 (2011) 21–40

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dividend policy, the model recognises that tax rates on personal income differ across both investors and forms of income, allows for the deferral option on capital gains tax by reducing the effective tax rate, and considers both classical and dividend imputation tax systems.4 Thirdly, the model recognises that the level of dividends and interest affects the need for share issues, with their associated share issue costs (which discourages dividends and interest beyond the point at which share issues are induced). Fourthly, the model recognises that the level of dividends and interest affects the level of “internally-financed” investment, which may have negative NPV (and which encourages dividends and interest up to point at which such investment is avoided). Clearly, there are other aspects of debt and dividend policy that are not readily capable of being incorporated into this analysis, most particularly relating to agency issues and asymmetric information. So, our results are subject to that caveat. The paper commences by optimising dividend and debt policy for a given level of “externally-financed” investment, and then goes on to consider the implications of optimal debt and dividend policy for the level of such investment. 2. The model The firm's investments comprise those that are justified even if they are externally-financed (“externally-financed” investment) and those that are viable only when funded from internally-generated cash flow (“internally-financed” investment). The level of “internally-financed” investment is endogenous to this analysis, i.e., for a given level of “externally-financed” investment, smaller dividends and interest payments induce larger “internally-financed” investment. In respect of “externally-financed” investment, we start by treating it as exogenously determined. Define S0 as the current equity value of a firm, DIV1 as the dividend to be paid in one year, K1 as the share issue undertaken in one year to support the level of “externally-financed” investment at that time, i as the issue cost per $1 of K1, M1 as the level of “internallyfinanced” investment, Q1 as the NPV per $1 of M1 (which will not exceed zero5), S1 as the value of equity in one year if M1 is zero (the value of equity in one year exclusive of the effect of any “internally-financed” investment), and ke as the cost of equity capital. It follows that6 S0 =

EðDIV1 Þ−EðK1 Þð1 + iÞ + EðM1 Þð1 + Q1 Þ + EðS1 Þ 1 + ke

ð1Þ

Defining X1 as the unlevered post-company tax cash flow from operations in one year, INT1 as the interest payment at that time (which is subject to a corporate tax saving at the statutory corporate tax rate Tc), and RET1 as the part of X1 that is retained to finance new investments (of any type), it follows that7 DIV1 = X1 −INT1 ð1−Tc Þ−RET1

ð2Þ

Define N1 as the (exogenously determined) level of “externally-financed” investment in one year (being that justified even if it is externally financing), B0 as the debt market value now, B1 as the debt market value in one year, and L1 as follows8: L1 ≡N1 −ðB1 −B0 Þ−RET1

ð3Þ

4 The use of an effective capital gains tax rate to account for the deferral option is less sophisticated than the approach in Green and Hollifield (2003). However, even after making certain simplifying assumptions, the latter still requires a highly complex recursive approach to valuation. Furthermore, the deficiencies in using an effective capital gains tax rate are in part simply the risk of adopting the wrong effective rate, and the analysis later in this paper shows that the results are not particularly sensitive to errors here (essentially because statutory capital gains tax rates in the tax regimes examined here are low or zero). 5 A number of possible tax regimes will be considered shortly. Across these regimes, Q1 never exceeds zero. 6 It should be noted that if K1 is positive, then M1 = 0. Also, if M1 is positive, then K1 = 0. 7 This formulation treats the interest tax deduction as if it is certain to be immediately usable. However, at sufficiently high levels of debt, the deduction may not be usable or immediately usable because of non-cash tax deductions such as tax depreciation (DeAngelo and Masulis, 1980b) and by variability in a firm's taxable income (Graham, 2000). The corporate tax benefit of debt is then overstated and Graham (2000) shows that the extent of this effect is substantial. We will return to this point. 8 Since the cost of debt capital does not change, the market value of debt at any point is equal to its book value and therefore B1 − B0 is equal to the additional borrowing at time 1 (repayment if negative). Additional borrowing or repayments at various times are necessary to maintain the leverage ratio.

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If L1 is at least zero, then L1 = K1 and M1 is zero. If L1 is less than zero, then L1 = −M1 and K1 is zero. Accordingly, L1 = K1 − M1. Using Eqs. (2) and (3), Eq. (1) can then be written as follows: S0 = =

EðDIV1 Þ−EðL1 Þ−EðK1 Þi + EðM1 ÞQ1 + EðS1 Þ 1 + ke EðX1 Þ−INT1 ð1−Tc Þ−EðN1 Þ−B0 −EðK1 Þi + EðM1 ÞQ1 + EðB1 Þ + EðS1 Þ 1 + ke

Defining kd as the cost of debt, it follows that INT1 = kdB0. In addition, S0 + B0 = V0 and S1 + B1 = V1. It follows that V0 + S0 ke + B0 kd ð1−Tc Þ = EðX1 Þ−EðK1 Þi + EðM1 ÞQ1 −EðN1 Þ + EðV1 Þ and therefore V0 =

EðX1 Þ−EðK1 Þi + EðM1 ÞQ1 −EðN1 Þ + EðV1 Þ 1+

S0 V0

ke +

B0 V0

kd ð1−Tc Þ

The denominator term here is the weighted average cost of capital (WACC). If this is the same for all future periods, then successive substitution for terminal value yields ∞

V0 = ∑

t =1

EðXt Þ−EðKt Þi + EðMt ÞQ1 −EðNt Þ ð1 + WACC Þt

ð4Þ

So far, this is the standard model for valuing a firm (or project) subject only to the addition of the issue costs for share issues and the (possibly negative) NPV arising from “internally-financed” investment. Adopting the usual assumption that cash flows are expected to grow at rate g, Eq. (4) reduces to the following9: V0 =

EðX1 Þ−EðK1 Þi + EðM1 ÞQ1 −EðN1 Þ WACC−g

ð5Þ

Dividend and debt policy affect E(K1), E(M1) and WACC. So, the implications of debt and dividend policy for WACC must be considered. By definition WACC =

S0 B k + 0 kd ð1−Tc Þ V0 e V0

ð6Þ

The analysis should recognise that personal taxes exist, and that such tax rates may vary across both investors and forms of income. Since the cost of debt is empirically determinable, these factors will necessarily be allowed for. By contrast, the cost of equity is typically estimated by recourse to a model, and the model must therefore explicitly recognise these factors. A comprehensive model that does so is as follows (Lally, 1992; Cliffe and Marsden, 1992)10
 n ∑ E DIV1j Tdj

ke = Rf ð1−T Þ +

j=1

S0

+ ϕβe

ð7Þ

9 A widely used variant of Eq. (5) involves forecasting cash flows for each of the next T years after which the constant growth model is invoked (Koller et al., 2005; Copeland et al., 2005). In the interests of focusing upon optimal debt and dividend policy here, we adopt the simpler formulation reflected in Eq. (5). It should also be noted that the assumption of a constant growth rate in expected cash flows can be derived from various models, such as Xt = Xt − 1(1 + g)(1 + et), where et is mean zero and uncorrelated; or from the alternative model Xt = [E(X1) + εt](1 + g)t − 1 where εt is mean zero. The first model involves positive correlation in the sequence of cash flows whilst the second model may or may not (and will not if εt is uncorrelated). It should also be noted that the size of N1 relative to X1 will affect the expected growth rate g, and Gordon and Shapiro (1956) formalise such a relationship. 10 The model extends Brennan (1970) to allow for the possibility of dividends being taxed differently to that of interest.

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where Rf is the risk free rate, ϕ is the market risk premium in this version of the CAPM, βe is the equity beta, and DIV1j is the time 1 dividend subject to type j tax treatment.11 In addition the tax parameters T and Tdj are weighted averages across investors as follows T = ∑ wi i

" # "j # ti −tgi t −tgi and Tdj = ∑wi di 1−tgi 1−tgi

ð8Þ

where ti, tgi and tjdi are investor i's tax rates on interest, capital gains, and cash dividends subject to type j tax treatment respectively.12 In respect of the cost of debt kd, this is the sum of the risk free rate Rf and the debt premium p. Substitution of this result and Eq. (7) into Eq. (6) yields the following result:
  ∑E DIV1j Tdj S0 S0 B
WACC = Rf ð1−T Þ + ϕβe + + 0 Rf + p ð1−Tc Þ V0 V0 V0 V0
T ∑E DIV 1j dj S B B + 0 Rf ðT−Tc Þ + 0 pð1−Tc Þ = Rf ð1−T Þ + 0 ϕβe + V0 V0 V0 V0

ð9Þ

In respect of the equity beta, the (standard) assumption that WACC is constant over time implies that the leverage ratio is constant over time. Assuming no systematic risk on debt, the appropriate formula under a classical tax regime is then as follows " βe = βa

Rf Tc B 1− 1+ S 1 + Rf

!#

where βa is the equity beta in the absence of debt (Miles and Ezzell, 1985).13 By contrast, under a tax regime in which debt imparts no tax benefit (because the corporate tax advantage is offset by the personal tax disadvantage), the tax term disappears to yield the following result:   B βe = βa 1 + S The difference between these last two formulations is slight, and therefore the simpler model (the last equation) is preferred. Substitution of the last equation into Eq. (9) then yields the following result:

WACC = Rf ð1−T Þ + ϕβa +


 ∑E DIVij Tdj V0

+

B0 B R ðT−Tc Þ + 0 pð1−Tc Þ V0 f V0

The first two terms on the RHS are the cost of capital in the absence of dividends or interest payments (and are designated k), the third term reflects the personal tax effect of dividends, the fourth term reflects

11 Different tax treatment of dividends could arise for a number of reasons. For example, in a dividend imputation regime, dividends with imputation credits are taxed differently to those without them. Alternatively, the firm may have the option of making the dividend payment in the form of share repurchases and the latter are generally taxed differently to conventional dividend payments. 12 The weight wi for investor i reflects both the proportion of the value of all risky assets held by them (vi) and the risk premium to variance ratio for their chosen portfolio relative to that of other investors, and the latter reflects both their degree of risk aversion and the tax rates to which they are subject on various assets (see Lally, 1992, Appendix 1). In respect of risk aversion, more riskaverse investors will hold portfolios with a higher risk premium to variance ratio. In respect of tax rates, investors with a tax rate on bonds relative to equities that is high relative to other investors (being investors on high incomes) will tilt towards equities rather than bonds, which raises their value for vi and therefore raises T. So the value of T tends to reflect the tax rates of investors on high incomes. This demand-side effect is explicit in the analysis of DeAngelo and Masulis (1980a,b) because they explicitly model investor behaviour rather than invoke a CAPM, which reflects investor behaviour. 13 A widely used alternative formula is that of Hamada (1972). However, Hamada's formula assumes that the debt level (rather than leverage) is constant over time and therefore is not appropriate here. In respect of systematic risk on debt, recognition of this simply leads to the debt premium in subsequent equations being replaced by the premium net of the systematic risk component, and any estimates of the debt premium would then have to be reduced. The analysis later in the paper does this.

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M. Lally / Pacific-Basin Finance Journal 19 (2011) 21–40

the net tax effect of interest, and the last term reflects the adverse debt premium effect from debt finance. Substitution of the last equation into Eq. (5), and solving for V0, yields the following result:

V0 =


 EðX1 Þ−EðN1 Þ−EðK1 Þi + EðM1 ÞQ1 −∑E DIV1j Tdj −B0 Rf ðT−Tc Þ−B0 pð1−Tc Þ k−g

ð10Þ

All of the effects of dividend and debt policy are now embodied in the last five terms of the numerator. The value maximising policy then maximises the sum of these five terms. The last three terms are determined by the level of dividends and interest, whilst the preceding two terms depend upon the level of retention as shown in Eq. (3), which in turn depends upon the level of dividends and interest as shown in Eq. (2). So, we solve Eq. (2) for RET1 and substitute it into Eq. (3). The result is thus: h i K1 = max N1 −ðB1 −B0 Þ−X1 + INT1 ð1−Tc Þ + ∑DIV1j ; 0

ð11Þ

h i M1 = max X1 + ðB1 −B0 Þ−N1 −INT1 ð1−Tc Þ−∑DIV1j ; 0

ð12Þ

Our valuation framework is now Eq. (10) subject to Eqs. (11) and (12), and allows dividend, debt and investment policy to be simultaneously optimised. We now apply the model to particular tax regimes. 3. Application to particular tax regimes 3.1. The MM tax regime We start with the simplest tax regime examined in the literature, in which debt generates a corporate tax deduction whilst personal tax rates are the same on all forms of personal income (Modigliani and Miller, 1958, 1961, 1963). Since personal tax rates are of this form, Tdj = T = 0 and therefore Eq. (10) reduces to the following:

V0 =

EðX1 Þ−EðN1 Þ−EðK1 Þi + EðM1 ÞQ1 + B0 Rf Tc −B0 pð1−Tc Þ k−g

ð13Þ

Modigliani and Miller (1958) also assume that debt is risk free and therefore that p = 0. Modigliani and Miller (1961) also assume that i = 0. In respect of Q1, they offer no explicit statement. However, consistent with the simple nature of the tax regime assumed by them, it might be assumed that dividends received by a company are not subject to corporate taxation. Thus, if a firm purchases shares in another company, the stream of dividends that it receives and passes back to its shareholders is identical to that arising to its shareholders if they directly purchased such shares. Since $1 invested directly by shareholders has a market value of $1, then $1 invested by a firm in the same way must add $1 to the market value of the firm. Thus, Q1 = 0. Substitution of these values for Q1, p and i into Eq. (13) yields the following:

V0 =

EðX1 Þ−EðN1 Þ + B0 Rf Tc k−g

In this case, dividends are irrelevant and the value is maximised by maximising debt so as to maximise the corporate tax deductions on interest. These conclusions match those of Modigliani and Miller (1958, 1961, 1963).14 14 However, the analysis in Modigliani and Miller (1958, 1961, 1963) is not a special case of Eq. (10) because Eq. (10) assumes constant market value leverage whereas Modigliani and Miller (1958, 1963) assume a constant dollar level of debt.

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3.2. A classical tax regime We now consider more realistic tax regimes, starting with a regime in which dividend imputation is not present (US). Both dividends and capital gains are generally taxable, and at the same statutory rate.15 However, capital gains are taxed only upon realisation and this deferral opportunity reduces the effective tax rate by about 50% (Protopapadakis, 1983; Green and Hollifield, 2003). In addition, defacto dividends can be paid without limit in the form of open-market share repurchases.16 As shown in Appendix A, an investor's tax rate on share repurchases is approximately equal to their effective tax rate on capital gains. So, in the absence of any restriction on the level of share repurchases, share repurchases are a superior means of disbursing cash flows to shareholders than conventional dividends and we therefore need only consider this type of dividend.17 Furthermore, following Eq. (8), the value for Td for this type of dividend is " # tgi −tgi Td = ∑ wi =0 1−tgi i

ð14Þ

In respect of Q1, being the NPV arising from investments beyond the level warranted if external finance is used, the best option amongst financial assets appears to be in the equity of other firms (due to the exemption of most of the resulting inter-corporate dividends from corporate taxation). In particular, only 20% of the dividends flowing from such an investment by a firm are subject to corporate tax, at the company tax rate Tc. Thus, if a company purchases shares in another company, the stream of dividends that can be passed back to its shareholders is proportion (1 −.20Tc) of that arising if the shareholders directly purchased such shares. Since $1 invested directly by shareholders has market value $1, then $1 invested by a firm in the same way must add $1(1 −.20Tc) to the market value of the firm. Thus, Q1 = −.20Tc.18Substitution of these results for Q1 and Td into Eq. (10) yields the following result: V0 =

EðX1 Þ−EðN1 Þ−EðK1 Þi−:20Tc EðM1 Þ−B0 Rf ðT−Tc Þ−B0 pð1−Tc Þ k−g

ð15Þ

To determine optimal dividend and debt policy, we start with dividend policy. This affects only K1 and M1. Following Eqs. (11) and (12), for a given level of debt, the optimal level of dividends is that which ensures that M1 = 0 and K1 are minimised, i.e., a residual dividend policy.19,20 So, E(M1) = 0 and E(K1) are minimised given the level of debt. Turning now to debt policy, and given this conditionally optimal (residual) dividend policy, debt policy should be chosen to maximise the sum of the third, fifth and sixth 15

Taxes may be avoided in certain cases, such as by investing via tax-exempt vehicles. Prior to 1982, firms may have been constrained from undertaking significant open-market repurchases out of fear of being charged with stock price manipulation by the SEC. However, the SEC's adoption of Rule 10b-18 in 1982 appears to have removed that concern (Grullon and Michaely, 2002, Section 6). 17 Green and Hollifield (2003) reach the same conclusion. Furthermore, the superiority of repurchases is consistent with their gradual supplanting of conventional dividends (Skinner, 2008). 18 Corporate investment in taxable bonds would give rise to corporate tax at the time of receiving interest, and further taxation when the interest was passed through to the firm's shareholders (even in the form of share repurchases), whereas shareholders who directly purchased such bonds would experience only one layer of taxation at their ordinary tax rate (which would not exceed the corporate tax rate in the US). So, Q1 is likely to be inferior to that for investment into equities. Alternatively, corporate investment into tax-exempt bonds would give rise to taxation at the time of passing through the interest to shareholders (even in the form of share repurchases) whereas shareholders who directly purchased such bonds would experience no taxation. So, Q1 is again likely to be inferior to that for investment in equities. However, if there are investments in real assets with NPVs between zero and −.20Tc, these would supplant investment in the equity of other firms and Q1 would then lie between 0 and −.20Tc. Furthermore, investments of this kind with negative NPV would be liquidated and the funds used to substitute for external equity issues should they ever be required, and this would further raise Q1 towards zero. However, since Q1 is still negative, the following analysis shows that dividend policy should be used to ensure that M1 = 0, and therefore the particular value of Q1 becomes irrelevant so long as it is negative. Nevertheless, for illustrative purposes, we use its lower bound of Q1 = −.20Tc. 19 Eq. (12) reveals that M1 can always be driven to zero by paying sufficiently large dividends. However, Eq. (11) shows that, even if dividends are reduced to zero, K1 may still be positive for a sufficiently low value for X1. 20 Green and Hollifield (2003, pp. 186–187) also conclude that dividends are superior to retention. However, they assume certainty and that any cash flows retained by the firm are invested in bonds. So, the analysis in the present paper has greater generality. 16

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terms in the numerator of Eq. (15), which involve the cost of share issues, the net tax effect of debt and the debt premium effect. Clearly, if T is at least the corporate tax rate Tc, then the last such term is negative at any positive debt level, the second term is zero or negative, and the first is aggravated by debt; consequently, the optimal debt level would be zero. On the other hand, if T is less than the corporate tax rate Tc, then debt may be desirable at some level because the net tax effect of debt is now positive and this may outweigh the adverse effects of debt at some debt levels. In summary, within the US tax regime, dividends should be strictly residual and in the form of only share repurchases, and the optimal level of debt should maximise the sum of the tax benefit net of the debt premium effect and the cost of share issues. 3.3. A dividend imputation regime We now turn to a tax regime in which dividend imputation operates, and focus upon a regime of the New Zealand type. If dividends are paid, and imputation credits are available, then they should be attached to the maximum possible extent. So, leaving aside share repurchases, dividends are effectively of two types: those with full imputation credits attached (paid first) and those without imputation credits.21 For fully imputed dividends (type 1), Lally (2000) shows that  Td1 = T−ð1−T ÞU

Tc 1−Tc

 ð16Þ

where U is the across-investor average utilisation rate for imputation credits (1 for investors who can fully utilise the credits and zero for those who cannot use them at all). Since this version of the CAPM assumes that national equity markets are fully segmented, and therefore closed to foreign investors, foreign investors (who cannot fully utilise the credits) should be ignored in choosing an estimate for U. The only other class of investors with a utilisation rate less than 1 are tax-exempt investors, who are small in New Zealand. This implies a value for U close to 1. Using the approximation of U = 1, Eq. (16) then reduces to the following: Td1 =

T−Tc 1−Tc

For unimputed dividends (type 2), Td2 = T. A third class of dividends is also available: defacto dividends can be paid in the form of on-market share repurchases (type 3 dividends).22 In respect of these share repurchases, and by contrast with the US case, the statutory rate applicable to the cash proceeds in New Zealand would be zero. Furthermore, and again by contrast with the US case, most New Zealand investors are exempt or effectively exempt from capital gains tax (with the remainder only subject to capital gains because the “dividend” was received by an intermediary entity that was subject to capital gains tax). Despite these differences, the analysis in Appendix A is still valid; the fact that all recipients of the cash proceeds would be exempt from capital gains tax and that some investors in general would be exempt from capital gains tax simply gives rise to particular numerical values for their statutory and effective tax rates rather than invalidating the analysis in Appendix A. So, the relevant tax rate for all investors is still their effective capital gains tax rate. Accordingly, as shown in the previous section, Td3 = 0. In respect of Q1, New Zealand firms can invest unlimited sums in the shares of other firms paying fully imputed dividends. Receipt of a fully imputed dividend implies that the recipient corporation pays no company tax on it. Thus, the stream of dividends that it passes back to its shareholders is identical to that arising from the shareholders directly purchasing such shares. Since $1 invested directly by shareholders 21 If a dividend is paid in excess of the level that can be fully imputed, this dividend can be considered to be two dividends, one of which has full imputation credits attached and the other without imputation credits. 22 The only restrictions on the level of these share repurchases relate to preserving the solvency of the company. However, onmarket repurchases beyond the level of the company's “subscribed capital” do induce a reduction in the company's imputation credits whilst those below this threshold are exempt from this effect (see section CD24 of the Income Tax Act 2007). In respect of off-market share repurchases, these are subject to certain restrictions (as detailed in section CD22 of the Act) that seem to be designed to preclude defacto dividends. So, we can ignore these.

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has market value $1, then $1 invested by a firm in the same way must add $1 to the market value of the firm. Thus, Q1 = 0. Substitution of these values for Td1, Td2, Td3 and Q1 into Eq. (10) yields the following result:   T−Tc EðX1 Þ−EðN1 Þ−EðK1 Þi−EðDIV11 Þ −EðDIV12 ÞT−B0 Rf ðT−Tc Þ−B0 pð1−Tc Þ 1−Tc V0 = k−g

ð17Þ

We now seek to determine optimal dividend and debt policy. If T exceeds Tc, then neither conventional dividends with or without full imputation credits nor debt will be desirable because the tax effects shown in Eq. (17) are negative in all three cases, E(K1) may be raised (which is undesirable), and the adverse debt premium effect arises in the case of using debt. In addition, dividends in the form of share repurchases have no valuation effect so long as they are not so high as to induce additional share issues (i.e., raise K1) and are undesirable beyond that point. If T is equal to Tc, then conventional dividends without imputation credits and debt are still undesirable, and dividends in the form of share repurchases are still irrelevant so long as they do not induce additional share issues, for the reasons given in the previous paragraph. However, in respect of conventional dividends with full imputation credits, these are now irrelevant so long as they are not so high as to induce additional share issues. Finally, if T is less than Tc, then fully imputed (type 1) dividends that do not induce additional share issues (raise K1) will be desirable because the tax effect shown in Eq. (17) will be positive. Also, additional fully imputed dividends may be desirable, and will be if the net tax effect outweighs the additional share issue costs. Unimputed dividends would be undesirable because the tax effect shown in Eq. (17) would be undesirable (the coefficient T on these dividends would be positive). Dividends in the form of share repurchases would again have no valuation impact so long as they are not so high as to increase the level of share issues (and are undesirable beyond that point). In respect of debt, this might be optimal because the tax effect shown in Eq. (17) would be positive and this might outweigh the debt premium effect and any adverse effect upon E(K1). However, if fully imputed dividends were paid, the tax benefits from interest would simply come at the expense of those from fully imputed dividends.23 The other two effects of debt are negative. So, it could not be optimal to simultaneously pay fully imputed dividends and interest. Accordingly the optimal policy would be the better of the following: no debt coupled with the maximum level of fully imputed dividends, no debt coupled with the maximum level of fully imputed dividends that do not induce additional share issues, or no dividends coupled with the debt level that maximised the sum of the debt sensitive terms in the numerator of Eq. (17).24 In summary, if T exceeds Tc, then both conventional dividends and debt will be undesirable, because the tax effect is negative in both cases, and dividends in the form of share repurchases will be irrelevant so long as they are not so high as to induce share issues. If T is equal to Tc, then both debt and conventional dividends without imputation credits will be undesirable, and both conventional dividends with full imputation credits and dividends in the form of share repurchases will be irrelevant so long as they do not induce share issues. Finally, if T is less than Tc, then unimputed dividends will be undesirable, dividends in the form of share repurchases will be irrelevant so long as they are not so high as to induce share issues, and the optimal policy will be the better of the following: no debt coupled with the maximum level of fully imputed dividends, no debt coupled with the maximum level of fully imputed dividends subject to not inducing any additional share issues, or no dividends coupled with the debt level that maximised the sum of the debt sensitive terms in the numerator of Eq. (17). 23 Raising INT1 by $1 reduces the available imputation credits by $1Tc, and therefore reduces the level of fully imputed dividends that can be paid by $1Tc(1 − Tc)/Tc = $1(1 − Tc). Consequently, if fully imputed dividends are being paid, the effect of raising interest payments by $1 is to raise the fourth term, and lower the sixth term, in the numerator of Eq. (17) by matching amounts. 24 The last of these options deals with the possibility that the level of fully imputed dividends implied by the better of the first two options is so low that debt dominates dividends, because the effective absence of tax benefits on that part of the debt whose tax benefits simply come at the expense of lower imputation credits, coupled with the adverse effects from that level of debt (as detailed above), is offset by the tax benefits on the additional debt beyond that point.

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4. Some examples 4.1. A classical tax regime We now consider an example based upon the US tax regime discussed in Section 3.2. In respect of tax rates, dividends and long-term capital gains are taxed at 15%, interest is taxed at marginal rates up to 35%, and the corporate tax rate is 35% (Berk and DeMarzo, 2007, Table 15.3).25 However capital gains taxes are paid only on realisation and, as noted earlier, this reduces the effective tax rate by about 50%. Furthermore, in view of the range in tax rates on interest and the fact that T tends to reflect the tax rates of investors with high incomes (see footnote 11), we adopt an average rate on interest of 30%.26 Consistent with this, and following Eq. (8), the value for T is as follows: " # ti −tgi :30−:075 = :24 T = ∑ wi = 1−:075 1−tgi i Also, Q1 = −.20(.35) = −0.07. Finally, suppose also that X1 is uniformly distributed on [0, $10m], N1 = $1.8m for certain, the issue costs post-company tax are i = .05, Rf = .065, g = .04 and k = .10. Substitution of these parameter values into Eqs. (11), (12) and (15) yields the following result: h i K1 = max D1:8m−X1 −:04B0 + B0 ð:065 + pÞð0:65Þ + ∑DIV1j ;0

ð18Þ

h i M1 = max X1 −D1:8m + :04B0 −B0 ð:065 + pÞð0:65Þ−∑DIV1j ;0

ð19Þ

V0 =

D3:2m−:05EðK1 Þ−:07EðM1 Þ−:065B0 ð:24−:35Þ−B0 pð0:65Þ :10−:04

ð20Þ

We start with DIV1 = B0 = 0. Given that X1 is uniformly distributed on [0, $10m], Eqs. (8) and (9) imply that E(K1) = $0.162m and E(M1) = $3.36m. Substitution of these results into Eq. (20) yields the following result:

V0 =

D3:2m−:05ðD0:162mÞ−:07ðD3:36mÞ = D49:3m :10−:04

ð21Þ

Turning now to optimal policy, and as shown in Section 3.2, the optimal dividend policy is residual dividends (yielding M1 = 0 and minimal K1 for a given debt level) whilst the optimal debt level maximises V0 conditional upon the dividend policy just described. For values of the debt risk premium p less than .011, the sum of the last two terms in the numerator of Eq. (20) is positive, and values for p within this range are possible for at least moderate leverage levels (so long as the recent sharp rise in corporate debt premiums is ignored). Some level of debt may then be optimal. Thus, to explore the issue further, it is necessary to specify a relationship between p and B0. Almeida and Philippon (2007, Table I) give risk premiums for bonds of various credit ratings, for a range of maturities, and we use the results for five year bonds. They also give estimates of leverages associated with those credit ratings from a number of studies (ibid,

25 These are federal tax rates only and state taxes also apply. However, in view of the considerable variation in state tax rates (some of them are zero) and their much lower level, we ignore them here. We also assume that all capital gains are long-term, which requires a holding period of at least 12 months (short-term capital gains are taxed much more highly). Green and Hollifield (2003, p. 201) act likewise in respect of both of these points. 26 Graham (2000, p. 1913) also estimates the average tax rate on interest at 30% based on the 1993 situation, when the top marginal rate on interest was very similar to what it is currently (Berk and DeMarzo, 2007, Table 15.3). In addition, Green and Hollifield (2003) consider estimates of the average tax rate on interest of 28% and 35%.

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31

Table V) and we use the last of the results cited there.27 This permits a relationship between p and leverage to be specified. Clearly the relationship is non-linear and therefore Ln(p) is regressed on leverage to yield LnðpÞ = −5:79 + 4:42

B0 V0

ð22Þ

which implies that p rises from .003 at leverage of zero to .018 at leverage of 40% and .043 at leverage of 60%.28 With this relationship, the problem requires simultaneous solution of Eqs. (20) and (22) subject to Eqs. (18) and (19) and a residual dividend policy, to yield values for B0, p and V0. The mechanics of the solution process are as follows. Defining Q≡D1:8m + B0 ½ð:065 + pÞð0:65Þ−:04 then Eqs. (18) and (19) can be expressed as follows h i K1 = max Q −X1 + ∑DIV1j ;0 h i M1 = max X1 −Q −∑DIV1j ;0 and the residual dividend policy would then be as follows: If X1 ≤Q set DIV1j = 0; ⇒K1 = Q −X1 ; M1 = 0 If X1 ≥Q set DIV1j = X1 −Q; ⇒K1 = 0; M1 = 0 So  EðK1 Þ = probðX1 ≤Q Þ½Q−EðX1 ÞjX1 ≤Q  =

  Q Q Q2 = D10m 2 D20m

EðM1 Þ = 0 Substitution of the last two equations into Eq. (20) and simultaneously solving Eqs. (20) and (22) for B0, p and V0 yields B0 = $8.5m, p = .006 and V0 = $53.6m. Also, Q = $1.85m and therefore the expected dividends in the first year (in the form of share repurchases) are as follows: EðDIV1 Þ = probðX1 ≥Q Þ½EðX1 Þ−Q jX1 ≥Q Þ =

   D10m−Q D10m + Q −Q = D3:32m D10m 2

The valuation result here of V0 = $53.6m compares with V0 = $49.3m with no debt or dividends as shown in Eq. (21). So, the value increment from the optimal debt and dividend policies is 8.7%. Most of this is due to optimal dividend policy. In particular, if the debt level is set at zero and the optimal (residual) dividend policy is adopted, then V0 = $53.2m and hence optimal dividend policy contributes 80% of the 8.7% value gain. This significant value benefit from residual dividends arises from thereby avoiding “internally-financed” investments (with negative NPV). These results are not particularly sensitive to the values of parameters for which there is considerable uncertainty, most particularly T and the parameters in Eq. (22). Since higher values for these parameters would further reduce the already low value impact of the optimal debt level, consideration of lower values is suggested. Furthermore, the parameter values chosen above are likely to be too high rather than too low and this also points to consideration of lower values. In respect of the debt premium p, and as 27 The data predate the recent “credit crunch”. Use of data since the commencement of the “credit crunch” would simply reinforce the conclusions reached here that debt has marginal value at best. Furthermore, the data involve averaging over firms in a range of industries and therefore are merely illustrative of the appropriate relationship for a particular industry. 28 The logarithmic transformation shown in Eq. (20) appears to generate a linear relationship, consistent with recourse to the linear regression model shown in Eq. (22).

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Table 1 Summary of results under a classical tax regime. T = .24

Firm value with no debt/divs Optimal debt level Optimal expected dividends Firm value Value gain Value gain from optimal debt Value gain from optimal divs

T = .17

pc = − 5.79

pc = − 6.37

pc = − 5.79

pc = − 6.37

$49.3m $8.5m $3.32m $53.6m 8.7% 0.8% 7.9%

$49.3m $13.5m $3.31m $54.0m 9.5% 1.6% 7.9%

$49.3m $12.9m $3.28m $54.5m 10.5% 2.6% 7.9%

$49.3m $18.1m $3.26m $55.3m 12.2% 4.3% 7.9%

This table shows the optimal levels for debt and dividends along with the associated firm values in a classical tax system, under four possible combinations of parameter values. The impact of the optimal debt and dividend levels upon firm value (in% terms) is also shown.

discussed earlier in footnotes 2 and 12, we actually seek the premium net of the effect of both systematic risk and the default option held by equity holders. So, in respect of Eq. (22), we reduce the first coefficient from pc = −5.79 to −6.37, which would approximately halve the debt premium at any leverage level. In respect of T, the estimate of .24 takes no account of the existence of various tax-reducing schemes.29 For example, suppose that the existence of these schemes exempts 30% of investment income from tax, and therefore reduces the average tax rates on both interest income and capital gains by 30%. Accordingly the value for T shown earlier in this section would fall from .24 to .17.30 Table 1 shows the results from these four possible combinations of values for pc and T.31 Averaged across the four cases, the increase in value from optimal dividend and debt policies is 10.2% with only 2.3% of this coming from debt policy. The small benefit from optimal debt policy is not a reflection of the low level of optimal leverage; across, the four cases examined here, optimal leverage is 25%. In summary, within the US tax regime, debt generates a net tax benefit and some level of it is optimal (depending upon the size of the debt premium and the net tax benefit) in conjunction with residual dividends (paid in the form of only share repurchases). Across a range of possible combinations of values for the debt premium and personal tax rates, and relative to zero debt and dividends, the valuation gain from optimal debt and dividend policy is about 10% of firm value with about 80% of this coming from optimal dividend policy (in the form of residual dividends paid as share repurchases). This significant value benefit from paying residual dividends arises from thereby avoiding “internally-financed” investments (with negative NPV). The small benefit from optimal debt policy occurs in spite of the fact that the optimal leverage averages 25% across the cases examined here. These conclusions are premised upon interest generating an immediate corporate tax benefit in accordance with the statutory corporate tax rate. Thus, any allowance for the fact that interest deductions are not always immediately usable (as discussed in footnote 7) would give rise to even lower optimal debt levels and therefore even smaller value benefits from debt. This reinforces the conclusion that debt adds little to company value. 4.2. A dividend imputation tax regime We now consider an example from a tax regime featuring dividend imputation and focus upon the New Zealand tax regime discussed in Section 3.3. As discussed in that section, the optimal course of action depends inter alia upon whether the tax parameter T is more, equal to or less than the corporate tax rate Tc. 29 A prominent example is a Roth IRA scheme in which employees allocate part of their post-tax income to an account, which could be invested in a variety of assets including bonds or equities, and whose subsequent payouts are not taxable under certain conditions. However, there are limits on the amounts that can be invested and there may be penalties in the event of withdrawal before the investor reaches age 60 (Reilly and Brown, 2006, pp. 52–54). 30 The value for T is also sensitive to the extent to which the deferral option on capital gains tax lowers the effective tax rate. However, the effect here is much less. For example, suppose that the deferral option lowers the effective tax rate on capital gains by only 25% rather than 50%. The resulting value of T would then be .14 rather than .17. 31 The reduction in T may also raise the value of the firm in the absence of debt and dividends, via a reduction in the discount rate k. However, since our primary concern is with the value gains from optimal debt and dividend policy, we do not attempt to estimate this effect.

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33

So, we consider two possible cases, corresponding to the situation before and after certain recent changes in the tax regime (the introduction of the PIE tax regime from 1.10.2007 and the reduction in the corporate tax rate from 1.4.2008). We start with the current situation (from 1.4.2008). The effect of the PIE regime is to largely eliminate capital gains tax and lower the average tax rate on ordinary income (interest and gross dividends) to 30%.32 So, T = Tc = .30. As before, suppose that X1 is uniformly distributed on [0, $10m], N1 will be $1.8m for certain, the expected growth rate in cash flows is g = .04, the issue costs post-company tax are i = .05, k = .10, and Rf = .065. Substitution into Eq. (17), with omission of unimputed (type 2) dividends and debt, yields the following33: V0 =

D3:2m−:05EðK1 Þ :10−:04

ð23Þ

With zero dividends and debt, Eq. (11) implies that the level of share issues would be as follows: K1 = max½D1:8m−X1 ;0 Since X1 is uniformly distributed on [0, $10m], it follows that E(K1) = $0.162m. Substitution of this into Eq. (23) yields the following V0 =

D3:2m−:05ðD0:162mÞ = D53:2m :10−:04

Since T is equal to Tc then, as discussed in Section 3.3, the optimal course of action is no debt, no conventional unimputed dividends, and other dividends are irrelevant so long as they do not induce additional share issues. So, following this optimal policy, V0 = $53.2m as shown in the last equation. As before, this analysis presumes that interest deductions are always immediately usable. So, any allowance for the fact that they are not always immediately usable would simply reinforce the conclusion here that the optimal debt level is zero. The conclusion here that even fully imputed dividends are irrelevant (so long as they do not induce additional share issues) is rather remarkable, especially by comparison with the conclusion that residual dividends (in the form of share repurchases) are desirable in the US and add significantly to firm value. The explanation is thus. Under New Zealand's present tax regime, fully imputed dividends impart no valuation benefit because the net tax effect is zero and retained funds can be invested in assets with zero NPV (because there is no taxation of fully imputed inter-company dividends). By contrast, under the US tax regime, dividends in the form of share repurchases are desirable up to the residual level because the net tax effect is zero whilst retained funds could only be invested in assets with negative NPV (due to partial taxation of inter-company dividends). So, the explanation for the difference in conclusions concerning dividends lies in the tax treatment of inter-company dividends, with the US's partial taxation of intercompany dividends inducing a valuation gain from firms following a residual dividend policy. 4.3. Another dividend imputation tax regime We now turn to the New Zealand tax regime prevailing up to 1.10.2007, in which the company tax rate was Tc = .33 and the PIE regime did not apply. Under this tax regime, Lally and Marsden (2004) estimate the tax parameter T at .27. In addition, suppose as before that X1 is uniformly distributed on [0, $10m], N1 will be $1.8m for certain, the expected growth rate in cash flows is g = .04, the issue costs post-company

32 As discussed in footnote 11, the value for T is primarily determined by investors with high incomes. An investor in an investment fund that has elected to become a PIE (Portfolio Investment Entity) would be taxed at 30% on interest (as well as dividends inclusive of imputation credits) if their income was above $38,000 per annum, and 19.5% if their income was less. Otherwise investors would be taxed at 19.5%, 33% or 39% depending upon their income level. Thus, in view of the substantial use of PIEs by investors with high incomes, a good estimate of the average investor tax rate on interest would then be 30%. Accordingly, a good estimate of T would be .30. 33 Debt and unimputed dividends are omitted because they are undesirable as discussed in Section 3.3.

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tax are i = .05, k = .10, and Rf = .065.34 Substitution of these parameter values into Eq. (17), with the omission of unimputed dividends, yields the following35: V0 =

D3:2m−:05EðK1 Þ + :0896EðDIV11 Þ + :0039B0 −B0 pð0:67Þ :10−:04

ð24Þ

We start with zero dividends and debt. Eq. (11) implies that the level of share issues would be: K1 = max½D1:8m−X1 ;0 Since X1 is uniformly distributed on [0, $10m], it follows that E(K1) = $0.162m. Substitution of this into Eq. (24) along with DIV11 = 0 = B0 yields the following V0 =

D3:2m−:05ðD0:162mÞ = D53:2m :10−:04

ð25Þ

Since T is less than Tc then, as discussed in Section 3.3, the optimal course of action is the best of the following: no debt coupled with the maximum level of fully imputed dividends, no debt coupled with the maximum level of fully imputed dividends that do not induce additional share issues, or no dividends coupled with the debt level that maximises the sum of the debt sensitive terms in the numerator of Eq. (24). We start with the first option. With zero debt, the maximum level of fully imputed dividends would be u

DIV11 = IC1

  1−:33 :33

ð26Þ

where ICU 1 is the level of imputation credits absent debt, and is equal to the company tax paid to the New Zealand tax authorities absent debt. These imputation credits are related to the level of X1, and an upper bound would be about .60X1.36 Substitution of this upper bound into Eq. (26) yields DIV11 = 1.218X1. Since E(X1) = $5m it follows that E(DIV11) = $6.09m. In addition, following Eqs. (11) and (26): K1 = max½$1:8m−X1 + DIV11 ;0 = max½$1:8m−X1 + 1:218X1 ;0 = max½$1:8m + 0:218X1 ;0 Since X1 is uniformly distributed on [0, $10m], it follows that E(K1) = $2.89m. So the firm will be simultaneously paying dividends and making share issues. Substitution of these values for E(K1) and E(DIV11) along with B0 = 0 into Eq. (24) yields the following result: V0 =

D3:2m−:05ðD2:89mÞ + :0896ðD6:09mÞ = D60:02m :10−:04

ð27Þ

The second option is zero debt coupled with the maximum level of fully imputed dividends subject to these dividends not being so high as to induce share issues. Following Eq. (11) with zero debt K1 = max½D1:8m−X1 + DIV11 ;0 34 We use the same values for these parameters merely for convenience. The change in the tax regime may change the discount rate k and will change both the probability distribution of X1 and the relationship between ICu1 (the level of imputation credits in the absence of debt) and X1. However, it is still possible to specify the optimal debt and dividend policies for the assumed values for these parameters. The resulting firm value cannot be compared with that in either of the previous two sections. 35 Unimputed dividends are omitted because they should never be paid, as discussed in Section 3.3. 36 This would arise if all of the company's tax payments were to the New Zealand tax authority, and the costs of replacing existing fixed assets were large relative to the depreciation tax deductions. If replacement costs matched tax deductions then the company tax payments associated with X1 would be .49X1 at a tax rate of 33%, i.e., (X1 + .49X1)(.33) = .49X1. So, with some allowance for current replacement costs exceeding depreciation tax deductions (which are based upon historic costs), an upper bound of about .60X1 is suggested.

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Table 2 Summary of results under a dividend imputation regime with T b Tc. Imputation credits

0

0.2X1

0.4X1

0.6X1

Firm value with no divs/debt Optimal expected imputed divs Optimal unimputed divs Optimal share repurchases Optimal debt Firm value with optimal policy Value gain over no divs/debt Value gain from optimal debt Value gain from optimal divs

$53.2m 0 0 Irrelevant $4.3m $53.3m 0.2% 0.2% 0

$53.2m $2.03m 0 Irrelevant 0 $56.1m 5.5% 0 5.5%

$53.2m $4.06m 0 Irrelevant 0 $58.7m 10.3% 0 10.3%

$53.2m $6.09m 0 Irrelevant 0 $60.0m 12.8% 0 12.8%

This table shows the optimal levels for debt and three classes of dividends along with the associated firm values in an imputation tax system, under four possible levels of imputation credits. The impact of the optimal debt and dividend levels upon firm value (in % terms) is also shown.

and the dividend policy would then be as follows: If X1 ≤D1:8m set DIV11 = 0; ⇒K1 = D1:8m−X1 If X1 ≥D1:8m set DIV11 = X1 −D1:8m; ⇒K1 = 0 Since X1 is uniform on [0, $10m], this implies that E(DIV11) = $3.36m and E(K1) = $0.162m. Substitution of these values for E(K1) and E(DIV11) along with B0 = 0 into Eq. (24) yields the following result: V0 =

D3:2m−:05ðD0:162mÞ + :0896ðD3:36mÞ = D58:22m :10−:04

ð28Þ

Clearly this is inferior to the first option, and follows from the fact that the tax coefficient on DIV11 in Eq. (24) of .0896 exceeds the share issue cost of .05. The final option is no dividends coupled with the debt level that maximises the sum of the debt sensitive terms in the numerator of Eq. (24). Eq. (11) with zero dividends implies that K1 = max½D1:8m−X1 −:04B0 + B0 ð :065 + pÞð0:65Þ;0 Defining Q as Q≡D1:8m + B0 ½ð:065 + pÞð0:65Þ−:04 it follows that K1 = max½Q−X1 ;0 and therefore that  EðK1 Þ = probðX1 ≤Q Þ½Q −EðX1 ÞjX1 ≤Q  =

  Q Q Q2 = D10m 2 D20m

ð29Þ

Substitution of the last equation into Eq. (24) along with DIV11 = 0 and simultaneously solving Eqs. (22) and (24) for B0, p and V0 yield B0 = $4.3m, p = .004 and V0 = $53.3m. This is inferior to both of the previous options.37 So, across the three options, the best one is the first, i.e., zero debt and the maximum level of fully imputed dividends, yielding a firm value of $60.0m as shown in Eq. (27). This exceeds the $53.2m shown in 37 These results reflect the debt premium determined in accordance with Eq. (22), and this is likely to be overestimated for reasons discussed in Section 4.1. Halving the debt premium by reducing the first coefficient in Eq. (22) from −5.79 to −6.37 (as in Section 4.1) doubles the optimal debt level to B0 = $8.5m but raises firm value only slightly to V0 = $53.4m, which is still inferior to both of the first two options.

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Eq. (25) above (with no dividends or debt) by 12.8%, and reflects the tax benefits from paying fully imputed dividends (rather than retaining and investing the funds in zero NPV projects) net of the issue costs on the additional share issues resulting from doing so. These conclusions presume that the imputation credits available to the firm are at the highest possible level (of .60X1). Table 2 shows results for lower levels of imputation credits. The valuation gains from optimal debt and dividend policy are less and the optimal debt level remains zero except in the case of no or extremely low levels of imputation credits. As discussed in the previous section, these conclusions are premised upon interest generating an immediate corporate tax benefit in accordance with the statutory corporate tax rate. Thus, any allowance for the fact that interest deductions are not always immediately usable (as discussed in footnote 7) would reinforce the conclusion here that the optimal debt level is zero except possibly in the case of very low levels of imputation credits. In summary, conventional unimputed dividends are always undesirable, dividends in the form of share repurchases are irrelevant so long as they do not give rise to additional share issues, and the optimal policy involves a choice between no debt coupled with the maximum level of fully imputed dividends, no debt coupled with the maximum level of fully imputed dividends subject to not inducing any additional share issues, and debt coupled with no dividends. The analysis here shows that the first option always dominates the second, that debt is only preferred to fully imputed dividends if the level of imputation credits is at or very close to zero, that the value gain from paying the maximum level of fully imputed dividends could be as much as 13% of the firm's value, and that the value gain from debt if it is optimal to borrow is close to zero. The value benefit from paying fully imputed dividends (rather than retaining and investing the funds in zero NPV assets) arises from the resulting passing of imputation credits to investors, and is sufficiently large per $1 of dividend paid to warrant making share issues as well as paying fully imputed dividends. 5. The probability distribution for cash flows The analysis so far has invoked a probability distribution for X1, with the uniform distribution chosen simply because of its computational tractability. The need to invoke a probability distribution for X1 arises because share issue costs are recognised (unlike conventional DCF valuations of firms and projects) and the level of share issues depends upon the degree of variation in X1 around its expectation. This raises the question of whether alternative probability distributions with the same expectation would yield significantly different results. To assess this question, we consider an extreme alternative case in which all probability mass concentrates at the expectation of $5m, and redo some of the earlier analysis with this alternative probability distribution. In the first example considered in Section 4.1, relating to the US tax regime and involving the parameter values T = .24 and pc = −5.79, the firm's value absent debt or dividends rises only slightly from $49.3m to $49.6m, the optimal dividend policy is still residual, the optimal debt level rises only slightly from $8.5m to $8.9m, and the firm's value under optimal debt and dividend policy rises only slightly from $53.6m to $53.8m. So, optimal dividend policy is unchanged, optimal leverage rises only slightly from 15.8% to 16.5% and the value gain from optimal policy falls only slightly from 8.7% to 8.5%. In the example considered in Section 4.3, relating to the New Zealand tax regime prior to recent changes and involving ICu1 =.60X1, the firm's value absent debt or dividends rises only slightly from $53.2m to $53.3m, the optimal policy is still zero debt and payment of the maximum level of fully imputed dividends, and the value resulting from that optimal policy is still $60.0m. So, optimal policy is unchanged and the value gain from optimal policy falls only slightly from 12.8% to 12.6%. These examples reveal two points. Firstly, subject to maintaining the expectation, the choice of probability distribution for X1 is not important. Secondly, and consequently, it would seem to be sufficient to act as if all probability mass concentrates at the expectation. This has the particular advantage of not requiring any more information about X1 than is required in traditional DCF valuations of firms and projects. 6. Simultaneous analysis of debt and dividend policy The analysis so far has involved simultaneous choice of dividend and debt policy in order to maximise firm value. However, many alternative treatments of this issue seek to optimise one of these conditional upon some assumed policy in the other area. For example, Graham's analysis of optimal debt policy is conditional upon the firm's dividend policy being that which is actually employed (Graham, 2000, p. 1912). However, such conditional optimisation may lead to markedly suboptimal conclusions about the policy that is “optimised”.

M. Lally / Pacific-Basin Finance Journal 19 (2011) 21–40

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To illustrate this point, consider the tax regime and the example in Section 4.3 with ICu1 =.60X1, subject to the restriction that conventional dividends are zero. As shown in that section, the optimal debt policy subject to that restriction is debt of B0 = $4.3m, yielding a firm value of V0 = $53.3m. However, without the restriction, the optimal policy would have involved zero debt and the maximum level of fully imputed dividends, yielding a firm value of V0 = $60.0m. The loss in value resulting from the restriction is then 11%. Thus, partial optimisation may induce policy errors with significant valuation effects. 7. Implications for the level of externally-financed investment The analysis so far has also treated the level of “externally-financed” investment (that level of investment which is justified even if it is externally-financed) as exogenously determined. However, the assessment underlying the determination of the level of such investment necessarily assumes something about debt and dividend policy. So, if the analysis in this paper leads to a judgement about optimal debt and dividend policy that diverges from that assumed in determining the level of this “externally-financed” investment, then the level of this investment should be reassessed (in so far as the investment has not yet been made). Any such reassessment cannot lead to rejection of investment that has already been accepted because substitution of optimal debt and dividend policy for that previously assumed cannot reduce the assessed present value of the projects. However, such a reassessment might lead to the adoption of projects previously considered to be undesirable. To illustrate this point, suppose that the relevant tax regime is that currently prevailing in New Zealand, as described in Section 4.2. Consequently, the optimal level for both debt and conventional unimputed dividends is zero whilst fully imputed dividends and share repurchases are irrelevant so long as they do not induce additional share issues. By contrast, the assumed policies underlying the assessment of the level of “externally-financed” investment involve leverage of 35% and the payout of all residual cash flow in the form of conventional dividends (whether imputed or not). Furthermore, a recently rejected investment project involved an initial investment of $2m, expected unlevered post-company tax cash flows of $0.2m per year with an expected growth rate of g = .02 indefinitely, no imputation credits, a discount rate absent dividends or debt of k = .10, a corporate tax rate of Tc = .30, and a debt risk premium of p = .02.38 In addition, the prevailing risk free rate is Rf = .065. Following Eq. (17), with T = Tc = .30 under the current New Zealand tax regime and letting DIV12 denote the level of unimputed cash dividends during the first year, the present value of the project is as follows39: V0 =

D0:2m−EðDIV12 Þð:30Þ−:35V0 ð:02Þð1−:30Þ :10−:02

Also, the residual dividend policy described above implies that EðDIV12 Þ = D0:2m−INT1 ð1−:30Þ = D0:2m−½:085ð:35ÞV0 ð1−:30Þ Substitution of the last equation into its predecessor and solving for the present value of the project yields V0 = $1.78m. Consequently, the project has an NPV of −$0.22m, consistent with its rejection. However, as shown in Section 3.3, the optimal debt and dividend policy here involve zero debt and no conventional unimputed dividends. Following Eq. (17) with T = Tc, the present value of the project is then as follows40: V0 =

D0:2m = D2:5m :10−:02

This represents a 40% increase in the present value of the project, thereby raising the NPV of the project to $0.5m and therefore implying that the project should not have been rejected. Most of the value 38 The assumption of an indefinite life is merely for computational convenience. With a finite but long life for the assets, the results are virtually identical. 39 Future new investment, and hence future share issues, are both zero in the case of projects (as opposed to firms). 40 Again, future new investment, and hence future share issues, are both zero in the case of projects (as opposed to firms).

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improvement here comes from optimal dividend policy, i.e., if optimal dividend policy is adopted (no conventional unimputed dividends) but leverage of 35% is retained, then Eq. (17) implies that V0 =

D0:2m−:35V0 ð:02Þð1−:30Þ :10−:02

and therefore V0 = $2.36m. So, approximately 80% of the value increment arises from optimal dividend policy. In summary, the conclusions reached in this paper concerning optimal debt and dividend policy may deviate from those assumed in assessing the appropriate level of “externally-financed” investment, and substitution of the former for the latter may raise the optimal level of such investment. In the example considered, the present value of a proposed project was thereby raised by 40%, leading to acceptance rather than rejection of the project. 8. Conclusions This paper has simultaneously analysed optimal dividend policy, debt policy and the level of “externally-financed” investment within a multi-period DCF framework, and allows for differential personal taxation over both investors and types of income, the effect of dividends and interest on the level of share issues (and hence share issue costs), and the effect of dividends and interest on the level of “internally-financed” investment (with possibly negative NPV). Furthermore, examples of both classical and imputation tax regimes have been considered. In the classical tax regime considered here, corresponding to the US, debt generates a tax benefit and some level of it is optimal (depending upon the size of the debt premium and the tax benefit) in conjunction with residual dividends paid only in the form of share repurchases. Across a range of possible values for the debt premium and the average tax rate on interest, and relative to zero dividends and debt, the valuation gain from optimal debt and dividend policy is about 10% of firm value, with about 80% of this coming from optimal dividend policy. This significant value benefit from paying residual dividends arises from thereby avoiding “internally-financed” investments (with negative NPV). The small benefit from optimal debt policy occurs in spite of the fact that the optimal leverage averages 25% across the cases examined here. In the first of the imputation tax regimes considered here, corresponding to the current New Zealand regime, conventional unimputed dividends are not desirable and both fully imputed dividends and dividends in the form of share repurchases are neutral so long as they do not induce additional share issues. In addition, debt is no longer desirable because the net tax effect is now zero and the debt premium effect is adverse. In the second of the imputation tax regimes considered here, corresponding to New Zealand prior to the recent reduction in the corporate tax rate and the introduction of the PIE tax regime, conventional unimputed dividends are always undesirable, dividends in the form of share repurchases are irrelevant so long as they do not give rise to additional share issues, and the optimal policy involves a choice between debt and the maximum level of fully imputed dividends with debt preferred only if imputation credits are at or very close to zero. Furthermore, if imputation credits are present, the value gain from paying the maximum level of fully imputed dividends could be as much as about 13% of the firm's value, whilst the value gain from debt if it is optimal to borrow is close to zero. The value benefit from paying fully imputed dividends (rather than retaining and investing the funds in zero NPV assets) arises from the resulting passing of imputation credits to investors, and is sufficiently large per $1 of dividend paid to warrant simultaneously paying fully imputed dividends and making share issues. Across the three tax regimes considered, two points stand out: debt contributes little or nothing to firm value whilst dividends in the optimal form may raise firm value by as much as 13%. Having optimised debt and dividend policy for a given level of “externally-financed” investment, the paper also explores the implications of optimal dividend and debt policy for the level of “externallyfinanced” investment. The paper shows that substitution of optimal debt and dividend policy for any other policy assumed in evaluating such investments may significantly raise their present value, leading to acceptance rather than rejection of some such investment projects. Acknowledgement The comments of Glenn Boyle, Kurt Hess, Andrew Smith, Alastair Marsden, Steve Swidler, Peter Thomson, John Randal, participants at a 2008 seminar at the University of Waikato, participants at the 2009 New Zealand Finance Colloquium, and the journal referee, are gratefully acknowledged.

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Appendix A This appendix seeks to determine the tax rate on dividends that take the form of share repurchases and are treated by the tax authorities as share repurchases. The analysis recognises that repurchases impose not only an immediate capital gains tax upon some investors (those who sell the shares that the company buys) but a deferred obligation on all other investors arising from the increase in the company's share price. Suppose a firm with N shares and price per share P0 unexpectedly generates cash flow of X and immediately disburses it to shareholders via a share repurchase, involving m shares at the firm's exrepurchase share price of P1.41 So X = mP1. Also, since the unexpected cash flow is immediately disbursed, then the equity value is unchanged, i.e., NP0 = ðN−mÞP1 Thus NðP1 −P0 Þ = mP1 = X

ð30Þ

We focus upon an (average) investor i who sells shares under the repurchase in proportion to their holding immediately before the repurchase, and this proportion is denoted αi.42 The investor then receives αiX and the tax rate on this disbursement of αiX is the incremental taxes paid as a proportion of αiX. Incremental taxes are paid in respect of both the shares that are not sold to the company in the course of the share repurchase as well as those that are sold. For each of the shares that are not sold, totalling αi(N-m) shares, the share price rises from P0 to P1 as a result of the repurchase, and this capital gain generates a tax payment at the investor's effective capital gains tax rate tgi. For the αim shares that are sold to the company, the resulting tax payment is αim(P1 − H)tSi where tSi is the statutory capital gains tax rate and H is the average historic cost of the shares sold. However, sale of the shares to the company merely accelerates the eventual sale of the shares that would otherwise have occurred in the absence of a repurchase, and this alternative scenario would give rise to a capital gains tax obligation of αim(P0 − H)tgi. So, the tax obligation arising from the share repurchase is simply the increment. Thus, investor i's tax rate on the share repurchase (type 1 dividend) is as follows: 1 tdi

= =

h i αi ðN−mÞðP1 −P0 Þtgi + αi m ðP1 −H ÞtSi −ðP0 −H Þtgi ðN−mÞðP1 −P0 Þtgi + X

αX hi
 i m ðP1 −H Þ tgi + tSi −tgi −ðP0 −HÞtgi X h
i m ðP1 −P0 Þtgi + ðP1 −HÞ tSi −tgi

ðN−mÞðP1 −P0 Þtgi + X
 mðP1 −HÞ tSi −tgi NðP1 −P0 Þtgi = + X
X  m ð P −H Þ tSi −tgi NðP1 −P0 Þtgi 1 = + mP1 NðP1 −P0 Þ 
 H = tgi + tSi −tgi 1− P1 =

ð31Þ

X

using equation ð30Þ

If share repurchases occur shortly after the investor purchased the shares then H is approximately equal to P1, and therefore the tax rate on repurchases will be very close to tgi. As the interval from the average purchase date till the date of repurchase increases, then H tends to diverge from P1 and the tax rate on repurchases therefore tends to diverges from tgi. In a pro-rata repurchase, H will on average be less than P1 because share values tend to grow over time and therefore the tax rate on share repurchases will on 41 The assumption that an unexpected cash flow is immediately disbursed ensures that P0 does not impound any allowance for the cash flows that are disbursed, and therefore avoids confounding the tax rate on a repurchase with the tax rate on whatever form of disbursement the market had previously assumed. 42 This would literally occur under a pro-rata repurchase offer. However, even in the absence of a pro-rata repurchase offer, the matching proportion scenario characterises the average investor by definition.

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average exceed tgi in accordance with Eq. (31). However, in so far as shareholders have accumulated shares in the company over time, they may have the option of specifying the shares to be repurchased (and in the event of exercising that option would designate the shares with the largest value for H), and this would limit the extent to which the tax rate on repurchases exceeded tgi (see Dammon et al., 2001, footnote 3). For example, if H = .90P1, and tSi = 2tgi as discussed in Section 3.2, then Eq. (31) implies that the tax rate on share repurchases would be 1.10tgi. Furthermore, in an on-market repurchase, the shareholders who will tend to sell will be those with the highest value for H and this further limits the extent to which the tax rate on repurchases would tend to exceed tgi. So, to an acceptable degree of approximation, the investor's tax rate on repurchases can be treated as if it were equal to the investor's effective tax rate on capital gains. References Almeida, H., Philippon, T., 2007. The risk-adjusted cost of financial distress. The Journal of Finance 62, 2557–2586. Andrade, G., Kaplan, S., 1998. How costly is financial (not economic) distress? Evidence from highly-levered transactions that become distressed. The Journal of Finance 53, 1443–1493. Berk, J., DeMarzo, P., 2007. Corporate Finance. Pearson Addison Wesley. Boyle, G., 1996. Corporate investment and dividend tax imputation. The Financial Review 31, 465–482. Brennan, M., 1970. Taxes, market valuation and corporate financial policy. National Tax Journal 23, 417–427. Cliffe, C., Marsden, A., 1992. The effect of dividend imputation on company financing decisions and the cost of capital in New Zealand. Pacific Accounting Review 4, 1–30. Copeland, T., Weston, J., Shastri, K., 2005. Financial Theory and Corporate Policy, 4th ed. Pearson Addison Wesley. Dammon, R., Spatt, C., Zhang, H., 2001. Optimal consumption and investment with capital gains taxes. The Review of Financial Studies 14, 583–616. DeAngelo, H., Masulis, R., 1980a. Leverage and dividend irrelevancy under corporate and personal taxation. The Journal of Finance 35, 452–467. DeAngelo, H., Masulis, R., 1980b. Optimal capital structure under corporate and personal taxation. Journal of Financial Economics 8, 3–29. Fung, W., Theobald, M., 1984. Dividends and debt under alternative tax systems. Journal of Financial and Quantitative Analysis 19, 59–72. Gordon, M., Shapiro, E., 1956. Capital equipment analysis: the required rate of profit. Management Science 3, 102–110. Graham, J., 2000. How big are the tax benefits of debt. The Journal of Finance 55, 1901–1941. Green, R., Hollifield, B., 2003. The personal-tax advantages of equity. Journal of Financial Economics 67, 175–216. Grullon, G., Michaely, R., 2002. Dividends, share repurchases, and the substitution hypothesis. The Journal of Finance 57, 1649–1684. Hamada, R., 1972. The effect of the firm's capital structure on the systematic risk of common stocks. The Journal of Finance 27, 435–452. Koller, T., Goedhart, M., Wessels, D., 2005. Valuation: Measuring and Managing the Value of Companies, 4th ed. John Wiley & Sons. Lally, M., 1992. The CAPM under dividend imputation. Pacific Accounting Review 4, 31–44. Lally, M., 2000. Valuation of companies and projects under differential personal taxation. Pacific-Basin Finance Journal 8, 115–133. Lally, M., Marsden, A., 2004. Tax-adjusted market risk premiums in New Zealand: 1931–2002. Pacific-Basin Finance Journal 12, 291–310. Lintner, J., 1965. The valuation of risky assets and the selection of investments in stock portfolios and capital budgets. The Review of Economics and Statistics 47, 13–17. Masulis, R., Trueman, B., 1988. Corporate investment and dividend decisions under differential personal taxation. Journal of Financial and Quantitative Analysis 23, 369–385. Miles, J., Ezzell, J., 1985. Reformulating tax shield valuation: a note. The Journal of Finance 40, 1485–1492. Modigliani, F., Miller, M., 1958. The cost of capital, corporation finance and the theory of investment. The American Economic Review 48, 261–297. Modigliani, F., Miller, M., 1961. Dividend policy, growth and the valuation of shares. The Journal of Business 34, 411–433. Modigliani, F., Miller, M., 1963. Corporate income taxes and the cost of capital: a correction. The American Economic Review 53, 433–443. Mossin, J., 1966. Equilibrium in a capital asset market. Econometrica 24, 768–783. Protopapadakis, A., 1983. Some indirect evidence on effective capital gains taxes. The Journal of Business 56, 127–138. Reilly, F., Brown, K., 2006. Investment Analysis and Portfolio Management, 8th ed. Thomson South-Western. Sharpe, W., 1964. Capital asset prices: a theory of market equilibrium under conditions of risk. The Journal of Finance 19, 425–442. Skinner, D., 2008. The evolving relation between earnings, dividends and stock repurchases. Journal of Financial Economics 87, 582–609.