The Relationship Between Franking Credits and the Market Risk Premium

Transcription

1 The Relationship Between Franking Credits and the Market Risk Premium Stephen Gray * Jason Hall UQ Business School University o Queensland ABSTRACT In a dividend imputation tax system, equity investors have three potential sources o return: dividends, capital gains, and ranking (tax) credits. However, the standard procedures or estimating the market risk premium (MRP) or use in the CAPM, ignore the value o ranking credits. Oicer (1994) notes that i ranking credits do aect the corporate cost o capital, their value must be added to the standard estimates o MRP. In this paper, we explicitly derive the relationship between the value o ranking credits (gamma) and the MRP. We show that the standard parameter estimates that have been adopted in practice (especially by Australian regulators) violate this deterministic mathematical relationship. We also show how inormation on dividend yields and eective tax rates bounds the values that can be reasonably used or gamma and the MRP. We make recommendations or how estimates o the MRP should be adjusted to relect the value o ranking credits in an internally consistent manner. Current version: 15/07/05 * Corresponding author. UQ Business School, University o Queensland, Brisbane 4072, Australia. Ph: ; s.gray@business.uq.edu.au. The Australian Research Council provided unds or this project under Grant DP

2 The Relationship Between Franking Credits and the Market Risk Premium ABSTRACT In a dividend imputation tax system, equity investors have three potential sources o return: dividends, capital gains, and ranking (tax) credits. However, the standard procedures or estimating the market risk premium (MRP) or use in the CAPM, ignore the value o ranking credits. Oicer (1994) notes that i ranking credits do aect the corporate cost o capital, their value must be added to the standard estimates o MRP. In this paper, we explicitly derive the relationship between the value o ranking credits (gamma) and the MRP. We show that the standard parameter estimates that have been adopted in practice (especially by Australian regulators) violate this deterministic mathematical relationship. We also show how inormation on dividend yields and eective tax rates bounds the values that can be reasonably used or gamma and the MRP. We make recommendations or how estimates o the MRP should be adjusted to relect the value o ranking credits in an internally consistent manner. 2

3 1. Introduction It is standard practice to measure equity returns as dividends plus capital gains. Indeed, all known data sources measure equity returns in this way. However, in a dividend imputation system, there is potentially a third component o returns ranking credits. To the extent that ranking credits are valued by the market, this value must be added to the standard return measure. Oicer (1994) makes this point in the paper that develops the cost o capital ramework under a dividend imputation tax system. I ranking credits orm part o the equity return or individual irms, they must also orm a part o the market return. Thereore, i ranking credits have value, this value must be relected in estimates o the MRP. However, standard estimates o the MRP ignore ranking credits entirely. Hence, i the MRP is estimated using returns that are measured in the standard way (relecting dividends and capital gains only), the assumed value o ranking credits must be added to compute a grossed-up MRP, which can then be used in the CAPM to compute the cost o equity capital. In this paper, we review the mathematically deterministic relationship between the assumed value o ranking credits and the estimate o MRP. This is the ramework developed by Oicer (1994). Our ocus in this paper is not on how to best estimate the value o ranking credits or the market risk premium, but on the relationship between them. I ranking credits are assumed to have value, the MRP must relect this. It is inconsistent to assume that ranking credits are valuable such that they reduce corporate cost o equity, but then ignore them when estimating the market risk premium. The main contribution o the paper is that we derive an explicit relationship between the value o ranking credits (gamma), the MRP, and the assumed tax rate. I tax rates and the value o ranking credits are assumed to be high, the MRP must also be high. This is because higher tax payments generate more tax credits, which are more valuable i gamma ( γ ) is assumed to be high. This value o ranking credits must then be added to standard estimates o MRP. However, the assumptions about tax rates and the value o ranking credits must also be consistent with observed dividend yields. This is because ranking credits can only be distributed with dividend payments. It would be inconsistent to assume that large amounts o ranking credits are created and that these credits are valuable to investors i observed dividend yields were wholly insuicient to distribute these credits to investors. In this paper, we examine the mathematical relationship between these various parameters. We then examine how standard assumptions about parameter values would have to be changed in order to preserve internal consistency. In the next section, we revisit the Oicer (1994) ramework and provide an intuitive economic explanation o how ranking credits might aect the cost o capital o Australian irms. Section Three derives the deterministic mathematical relationship between gamma and MRP. In 3

4 Section Four, we draw several examples rom Australian regulatory determinations and demonstrate that the parameter values typically assumed are internally inconsistent. We also explore several methods or restoring internal consistency. Section Five examines attempts that have been made to adjust MRP estimates or the value o ranking credits and Section Six concludes. 2. Interpretation o the Oicer (1994) Framework Oicer (1994) develops a ramework or consistently deining the cost o capital and cash lows in a dividend imputation tax system. This ramework, and particularly the deinitions o weighted-average cost o capital (WACC), have been widely adopted in Australian practice. Oicer (1994) presents deinitions o WACC on a beore and ater corporate tax basis. In this section, we begin by examining his irst deinition o ater corporate tax cash lows and WACC, or ease o exposition. Under this deinition, the eect o ranking credits is incorporated in the discount rate the cost o equity capital. The same arguments apply regardless o which deinition o WACC is used and whether ranking credits are incorporated in the WACC or the cash lows. We subsequently examine the vanilla WACC speciication, under which the eect o ranking credits is incorporated in the cash lows. We demonstrate that the two approaches are entirely equivalent and lead to the same conclusions, based on the same intuition. Our points relate to the internal consistency o various parameter estimates. Using an estimate o γ in deining cash lows that is inconsistent with the estimate o MRP used to estimate WACC is just as problematic as i both are incorporated in the WACC estimate. Separating inconsistencies may make them harder to spot, but does not eliminate their eect. Moreover, Oicer demonstrates that all o his WACC/cash low deinitions produce identical results so long as they are applied consistently. Oicer (1994) begins by deining ater corporate tax cash lows as X o ( 1 T ), consistent with the standard textbook treatment. Here X o represents operating cash lows and T represents the relevant corporate tax rate. The deinition o the ater corporate tax discount rate that is consistent with this deinition o cash lows is stated in his Equation (7) as: r i S 1 T D = re + rd 1 V 1 T V ( 1 γ ) ( T ) (1) where: r i is the weighted-average cost o capital, relecting the tax deductibility o interest and the value o ranking credits, r E is the return on equity capital required by investors, r D is the return on debt capital required by investors, 4

5 S is the proportion o equity inance, V D is the proportion o debt inance, V T is the corporate tax rate, and γ is the value o ranking credits. In this ramework, r D is the return that debtholders require (beore personal tax) to compensate them or the risk involved in lending to the irm. Since these interest payments are tax deductible at the corporate level, the irm s ater-tax cost o debt capital is r D ( 1 T ). That is, i debtholders require a return o 7% and the corporate tax rate is 30%, the irm s ater-tax cost o debt is 4.9%. O the 7% required return, 4.9% is provided by the irm and 2.1% is eectively provided by government via the tax system. The same applies to the cost o equity. Here, r E is the return that equityholders require (beore personal tax) to compensate them or the risk involved in owning shares in the irm. In the Australian regulatory ramework, and in commercial practice, r E is usually estimated using the Capital Asset Pricing Model (CAPM). This provides an estimate o the return that the equityholders require. As is the case or debt, there is a dierence between the investors required return and what the irm must pay i a government tax subsidy is relevant. In particular, equityholders require a total ater corporate tax return o r E. This return potentially has three components: dividends, capital gains, and ranking credits. The irm is responsible or generating dividends and capital gains. Franking credits are paid by government via the tax system. Oicer s WACC ormula quantiies the proportion o r E that must be generated by the irm, and the proportion that is paid by government via the imputation tax system, irm s ater-tax cost o equity capital is r E 1 T 1 T ( 1 γ ) γ T 1 T 1 ( γ ) 1 T 1 T ( 1 γ ),. Thus, the. Indeed this is the key contribution o Oicer (1994). He derives the proportion o the required return on equity that must be generated by the irm via dividends and capital gains. O course, this point is well recognized in the academic and practitioner literature. Copeland, Koller and Murrin (2000, p. 134), or example, note that the WACC is the opportunity cost to all the capital providers weighted by their relative contribution to the company s total capital. They also note (p ) that, the opportunity cost to a class o investors equals the rate o return the investors could expect to earn on other investments o equivalent risk. The cost to the company equals the investors costs less any tax beneits received by the company (or example, the tax 5

6 shield provided by interest expense). In a dividend imputation system, the government may also subsidize equity returns via the payment o ranking tax credits. In the detailed numerical example in his Appendix, Oicer (1994, pp ), shows how the CAPM can be used to derive a required return on equity o 17.7% and that the irm s cost o equity is: r E 1 T 1 T = 17.7% ( 1 γ ) ( 1 0.5) = 13.4% (2) using the parameter values assumed in the example. That is, the imputation tax system has reduced the irm s cost o equity capital by 4.3% in this case. The value o this reduction in the irm s cost o equity is capitalized into the stock price. In this case, the value o equity increases rom $120 million (under a classical tax system) to $ million (under an imputation system in which γ = 0.5 ). Oicer demonstrates that the equityholders required return does not change. What changes is the proportion o this return that must be generated by the irm. In a classical system, the irm has to generate all o this return. In an imputation system, the government unds some o this required return (in act 4.3%) which reduces the irm s ater tax cost o equity rom 17.7% to 13.4%. That is, the CAPM tells us what return equityholders require (a return that is measured ater company tax but beore personal tax) and Oicer (1994) derives the proportion o that return that must be generated by the irm, 1 T 1 T ( 1 γ ). Alternatively, Oicer (1994) also shows how the value o ranking credits can be incorporated in the irm s cash lows rather than the discount rate. In his Equation (12), Oicer deines the vanilla WACC as: r = r S V iii E + r D D. V (3) This discount rate should be applied to cash lows deined as in his Equation (11): ( X X D )( 1 T ( 1 γ )) + X D 0, (4) where X D represents interest payments to debtholders. That is, under an imputation system, the cash low to equity holders is: 6

7 ( X ) 1 T ( 1 ) ( ). X 0 D γ (5) Without imputation ( γ = 0), the cash low to equity holders would be: ( X X D )( 1 ). 0 T (6) Thus, the component o the cash low to equity that is due to the value o ranking credits is the dierence between the two: ( X X D ) γ. 0 T (7) Thereore, the proportion o the total cash low to equity that is due to ranking credits is: ( X 0 X D ) γ T γ T = ( X X )( 1 T ( 1 γ )) 1 T ( 1 γ ). 0 D (8) This is the same proportion o the cost o equity that was due to ranking credits, as derived above. That is, i we preer to incorporate the value o ranking credits in the discount rate, we can conclude that γ T 1 T 1 ( γ ) proportion o the cost o equity is paid by the government via ranking credits. I we preer to put the value o ranking credits into the cash lows instead, we conclude that γ T 1 T 1 ( γ ) proportion o the total cash low to equity is paid by the government via ranking credits. In both cases, the balance, 1 T 1 T ( 1 γ ), must be generated by the irm itsel. 3. The Relationship Between Gamma and MRP 3.1. The Cost o Equity Capital The dominant commercial practice in Australia is to use the CAPM to estimate the return required by equityholders. This is the equilibrium return that they require on their equity investment ater corporate tax but beore personal tax. This return is deined as: kˆ e = r + ˆ ( k m r ) β e (9) 7

8 where kˆ e and kˆ m represent the expected returns on equity and the Australian market portolio respectively; r the risk-ree rate; and β e is the irm s equity beta. Oicer (1994) shows that the market return should include the value o ranking credits such that the expected return on equity is the total return, inclusive o dividends, capital gains and ranking credits. I market returns are deined in terms o dividends and capital gains only, Oicer (1994, eq. 18) shows that the value o ranking credits must be added back to obtain the total ater corporate tax market return. The CAPM then yields the total required return on equity, part o which must be provided by the irm and part o which is provided by government via ranking credits Return to Equityholders under Dividend Imputation Under a dividend imputation system, the expected return to equityholders comprises a return rom dividends and capital gains, plus the beneit o ranking credits, which can be expressed as: kˆ e = kˆ e 1 T 1 T + kˆ γt e ( 1 γ ) 1 T ( 1 γ ) (10) where kˆ e is the total required return on equity, which may be estimated using the CAPM, so long as the MRP includes the value o ranking credits; T is the corporate tax rate; and γ is the market value o ranking credits as a proportion o ranking credits created. This speciically recognizes that part o the return required by equityholders is provided by the irm via dividends and capital gains and part is provided by government via ranking credits. On the right hand side o the equation, the irst term represents the return on equity rom dividends and capital gains, while the second term represents the return on equity rom the beneits o dividend imputation. Allocating the total return to equityholders into these two components we can say that: Proportion o return rom dividends and capital gains = 1 T 1 T ( 1 γ ) (11) Proportion o return rom dividend imputation = γt 1 T ( 1 γ ) These proportions are based on Oicer (1994) and are illustrated in terms o discount rates and cash lows in Section 2. Table 1 and Figure 1 present these proportions or alternative values or the corporate tax rate and the value o ranking credits. For example, with a corporate tax rate o 8

9 30% and gamma set at 0.5, 82% o the total return required by (or cash low available to) equityholders is comprised o dividends and capital gains, while 18% o the total return (or cash low) consists o ranking beneits. Table 1: Proportion o returns to equityholders rom dividends and capital gains versus ranking credits under alternative values or the corporate tax rate and the value o ranking credits (gamma) Tax rate Gamma Proportion o returns attributable to dividends and capital gains (%) 10% % % % % Proportion o returns attributable to ranking credits (%) 10% % % % % Figure 1: Proportion o return on equity rom dividends and capital gains under alternative tax rates and the value o ranking credits (gamma) Tax rate 10% 20% 30% 40% 50% Gamma Franking Credits and the MRP Recall that implementation o the CAPM in this setting requires a market risk premium ( k ) ˆ that includes the value o ranking credits. This ramework, combined with the discussion m r 9

10 in Sections 3.1 and 3.2, implies that we can derive an expression or the market risk premium. Combining the equations in Sections 3.1 and 3.2 we have: r + ( kˆ r ) β = kˆ 1 T 1 T + kˆ γt e ( 1 γ ) 1 T ( 1 γ ) m e e. (12) For a irm with average systematic risk (β e = 1, representative o the market portolio), the cost o equity capital is: r + ( kˆ r ) = kˆ 1 T 1 T + kˆ γt e ( 1 γ ) 1 T ( 1 γ ) m e. (13) Consider the second term on the let-hand side o the equation, the market risk premium ( kˆ ) m r. This term represents the equityholders compensation or bearing systematic risk, and includes the value o ranking beneits. These ranking beneits are quantiied in the second term on the right-hand side o the equation,. Hence, i we subtract the riskree rate rom both sides o the equation, we have: ˆ Tγ k e 1 T ( 1 γ ) ( kˆ r ) m T = k ˆ 1 e 1 T r + kˆ e ( 1 γ ) 1 T ( 1 γ ) Risk premium rom Risk premium rom MRP = + dividends and capital gains ranking credits γt. (14) 1 T 1 T deine Recall that Oicer (1994) has shown that dividends and capital gains make up a proportion, ( 1 γ ), o the total return to equity, the balance due to the value o ranking credits. Next, MRP c to be the market risk premium including ranking credits and MRP dc to be the market risk premium rom dividends and capital gains only. Now, the total return on the market portolio, including ranking credits is MRP dc + r. Hence, MRP + r and the return rom dividends and capital gains only is c 10

11 Market return rom Market return rom 1 T dividends and capital = dividends, capital gains 1 T gains. and ranking credits.. ( 1 γ ) (15) This implies that: MRP + r = [ MRP + r ] 1 T 1 T ( 1 γ ) dc c, (16) in which case: MRP c = r + MRP dc ( 1 T )/[ 1 T ( 1 γ )] r. (17) Note that this ormulation is entirely consistent with the analysis o Oicer (1994, p. 9). In his Equation 17, Oicer states that the market return including the value o ranking credits is equal to the return as traditionally measured (dividends and capital gains only) plus the value o ranking credits: C r t = rt + γ P t t 1, (18) where r t is the all-inclusive market return, r t is the traditionally measured return, γ is the value o ranking credits, and Ct is the ranking credit yield. Oicer (1994) deines t P t 1 tax credits per share distributed at time t. However, this is a typographical error and C to be the amount o C t actually reers to credits created not distributed. It is well-known that γ is applied to ranking credits created not distributed, and this is also consistent with the detailed calculations in Oicer s appendix. Thus, C P t t 1 must be interpreted as the amount o ranking credits created per dollar o stock price. This is also consistent with the adjustment proposed by Lally (2004): r = r t t + Cdist UD, DIV (19) 11

12 where U is the value to the relevant investor o ranking credits once distributed, D is the cash dividend yield, and C dist DIV is the ratio o distributed imputation credits to dividends paid. Note that U applies to ranking credits that have been distributed, whereas γ applies to ranking credits created, so γ = U DR where DR represents the distribution rate, or the ratio o ranking credits distributed to ranking credits created C DR = C dist created. Thus, Lally s adjustment can be written as: U Cdist D DIV γ = DR DIV P Cdist = γ DIV C created P t 1 t 1. (20) which is identical to the Oicer adjustment in Equation (18). To establish the equivalence o our Equation (17) and the Oicer/Lally adjustment in Equation (18), irst note that the market return (ater company tax) measured in the standard way is: r = r + MRP t dc. (21) The amount o corporate tax paid on this return (and hence the amount o ranking credits created per dollar o stock price) is: T Ct ( r + MRP ) =. T rt = dc 1 T 1 T Pt 1 1 (22) Finally, the return including the value o ranking credits can be written as: r = r + MRP t c. (23) Substituting Equations (21)-(23) into Equation 17 yields: r + MRP = r + MRP + γ c dc T ( r + MRP ). dc 1 T (24) which implies that: 1 T. Then we compute corporate tax paid by multiplying this pre-tax return by the corporate tax rate, T Here, we gross-up the ater corporate tax return to a pre corporate tax return by dividing by ( )

13 r + MRP c = = ( r + MRP ) γ T 1+ 1 T 1 T ( ) ( 1 γ ) r + MRP dc dc 1 T, (25) which is equivalent to Equation (17). That is, the value o ranking credits must be added to the standard measure o the MRP. The required adjustment depends only on the assumptions made about the corporate tax rate and the value o ranking credits. 4. Consistency Between Parameters in Australian Practice Having established the adjustment that is required to properly incorporate the value o ranking credits and that our approach is exactly equivalent to the adjustment derived by Oicer (1994) and Lally (2004), we now examine Australian corporate practice. Although use o the CAPM is widespread, little inormation is available about the individual parameter estimates that are adopted by individual participants. For this reason, we ocus on regulatory determinations. Australian regulators have uniormly adopted the Oicer (1994) ramework or estimating the required return on capital. Their determinations also contain considerable detail about individual parameter estimates and the reasons or adopting them. Moreover, there are more than ten such regulatory bodies who collectively regulate inrastructure assets whose value exceeds $100 billion. This makes the Australian regulatory setting an ideal and important one in which to examine any cost o capital issue. The goal o this section is two old. First, we demonstrate that the set o parameter values that is commonly used in Australian corporate practice is inconsistent with Equation (17). That is, the parameters collectively are inconsistent with the ramework to which they apply! Second, we examine various alternatives or restoring consistency. This requires a change to the value o at least one parameter. We examine how each parameter in turn would have to be adjusted in order to restore consistency and examine the reasonableness o each adjustment in light o external data Interpretation o current practice It is common or the ollowing parameter estimates to be used in Australian regulatory determinations: MRP = 6%; T = 30% ; γ = Also, assume that the relevant risk-ree rate is 6%. It is unclear whether Australian regulators, in general, consider that this estimate o the MRP includes the value o ranking credits. As most regulatory determinations ignore this issue, we separately examine each possibility in turn. 13

14 MRP = 6% incorporates the value o ranking credits I the 6% estimate o MRP is assumed to include the value o ranking credits, Equation (17) implies that: MRP c = 6% = r + MRP dc ( 1 T ) [ 1 T ( 1 γ )] 6% + MRP dc r ( 1 0.3) [ 1 0.3( 1 0.5) ] 6%, (26) which implies that the MRP rom dividends and capital gains (the standard measure) is only 3.9%. In other words, in the absence o dividend imputation, the average stock on the Australian equity market would be expected to earn a return rom dividends and capital gains just 3.9% above the risk-ree rate. This is unreasonable, considering the historical evidence. For example, Dimson, Marsh and Staunton (2003) report that the average arithmetic mean o Australian equity returns (measured as dividends plus capital gains only) relative to Government bonds was 7.6% rom with a standard deviation o 19.0%, which is signiicantly dierent rom 3.9% at a level o just 2%. And out o the 16 developed markets studied, they report that only two had a market risk premium o less than 3.9% (based on dividends and capital gains). Also, the data sources that are used to justiy the estimate o 6% are generally based on dividends and capital gains only. For example, the Queensland Competition Authority recently adopted a 6% estimate primarily on the basis o historical averaging methodology in which ranking credits are ignored entirely 2. Moreover, this interpretation is also demonstrably inconsistent with observed dividend yields. I the risk-ree rate is 6% and the MRP estimate o 6% is assumed to include the value o ranking credits, the total return required on the market portolio is 12% ( + MRP = 6 % + 6% ) r. Recall that this is an ater corporate tax return. We have shown in Section 3.2 that application o the results in Oicer (1994) imply that i γ = 0. 5 and T = 30% equity investors receive about 18% o their return rom ranking credits and the remaining 82% rom dividends and capital gains. That is, the return rom ranking credits is assumed to be about 2.1% with the remainder coming rom dividends and capital gains. I we urther assume that ranking credits, once distributed, are valued at about 60% 2 QCA. (2004). Drat Determination Regulation o Electricity Distribution, p

15 o ace value 3 2.1%, the yield o ranking credits must be 3.5%. That is, the average irm in the 0.6 market portolio must distribute ranking credits with ace value o 3.5% o the stock price. At a corporate tax rate o 30%, with every $1 o dividends paid, ranking credits o 43 cents T 0.3 = 1 T can be distributed. Thereore, to generate a ranking credit yield o 3.5%, the 3.5% average irm must generate a dividend yield o 8.2%. That is, a $10 stock pays a dividend 0.43 o $0.82, with ranking credits o $0.35, i ully ranked. This ranking credit is then worth $0.21 to the relevant investor. To the extent that not all dividends are ully ranked, the aggregate dividend yield on the market portolio would have to be even higher than 8.2%. Since the observed dividend yield on the market portolio is an order o magnitude less than this, the assumptions o γ = 0. 5, T = 30% and MRP c = 6% are dramatically inconsistent with observed market data. Finally, note that oreign investors do not beneit rom ranking credits. Thus, setting the MRP to 6% including the value o ranking credits is equivalent to assuming that oreign investors will provide capital in return or a 3.9% risk premium on the average stock. Since this is demonstrably less than what has been obtained in every other domestic market, it ails the test o economic reasonableness. For all o these reasons, it seems impossible to sustain an argument that the 6% estimate o the MRP includes a 2.1% return rom ranking credits. MRP = 6% relects dividends and capital gains only I the 6% estimate o MRP is assumed to exclude the value o ranking credits, Equation (17) implies that: MRP c r + MRPdc = r = ( 1 T ) [ 1 T ( 1 γ )] ( 1 0.3) [ 1 0.3( 1 0.5) ] = 8.6%. 6% + 6% 6% (27) 3 Recall that gamma relects (i) the rate at which the ranking credits that are created by the payment o corporate tax are distributed to shareholders, and (ii) the value that the relevant shareholder places on each dollar o ranking credits they receive. It is common to assume that about 80% o created ranking credits are distributed and that, once distributed, ranking credits are worth about 60% o ace value to the relevant investor. ESCOSA document their use o a 60% estimate in the Drat Electricity Distribution Price Determination and the QCA (2004) uses 62.5% in the Drat Determination Regulation o Electricity Distribution. 15

16 that is, the MRP including the value o ranking credits is 8.6%. However, this is also dramatically inconsistent with observed data on dividend yields. Recall that i γ = 0.5 and T = 30%, about 18% o the total return comes via ranking credits. Thus, the return rom ranking credits in this case is about 2.6%. Using the same logic as the previous case, a dividend yield o 10% is required to distribute suicient ranking credits to warrant this return. Thus, however we interpret the MRP estimate o 6%, the standard set o parameter values produce results that are demonstrably inconsistent with each other and with observed data on dividend yields. In the remainder o this section, thereore, we explore ways o restoring consistency by altering parameter values Changing parameter values to restore consistency γ = 0 Setting the value o ranking credits to zero is the most straightorward and most complete way to restore consistency. In this case, a MRP o 6% is based on dividends and capital gains only. Observations pre- and post-imputation can be included in the same data set without adjustment. There are also no implications or how high or low dividend yields would have to be. Importantly, no other parameter estimates would have to change. Moreover, this is consistent with the most recent evidence rom market data 4 and rom dividend drop os 5. It is also perectly consistent with observed market practice. Truong, Partington and Peat (2005) survey 356 listed Australian irms about various corporate inance practices. All irms were included in the All Ordinaries Index in August 2004, Australian and not in the inance sector. On the question o how ranking credits were treated, 85% o respondents indicated that they made no adjustment or the value o ranking credits. Lonergan (2001) surveys expert valuation reports prepared in relation to takeovers. He reports that o 122 reports reviewed only 48 (or 39%) provided support showing how they had arrived at the WACC used in their reports. O these, 42 (or 88%) used the CAPM to compute the cost o equity capital and made no adjustment or dividend imputation. Only six reports made any sort o adjustment to relect dividend imputation. Furthermore, o the ew reports that did make an adjustment or the value o ranking credits, or all but one the ultimate eect on the value o the company was negligible or zero. Importantly, nearly hal o Lonergan s sample is rom ater the 4 Cannavan, Finn & Gray (2004). 5 Bellamy & Gray (2004). 16

17 1997 introduction o the 45-day rule that was introduced to prevent trading in ranking credits, yet only one expert report rom this period made any mention o the value o ranking credits. Lonergan (2001) also provides a list o conceptual grounds cited in reports or not adjusting or imputation credits, including: The value o ranking credits is dependent on the tax position o each individual shareholder; There is no evidence that acquirers o businesses will pay additional value or surplus ranking credits; There is little evidence that the value eects o dividend imputation are being included in valuations being undertaken by companies and investors or the broader market; Foreign shareholders are the marginal price-setters o the Australian market yet many such shareholders cannot avail themselves o the beneit o ranking credits; and There is a lack o certainty about uture dividend policies, the timing o taxation and dividend payments and consequently about ranking credits. Consequently, setting γ = 0 not only avoids the demonstrable internal inconsistency identiied above, but it is also perectly consistency with the dominant accepted market practice. MRP c = 0 The next possibility to consider is a reduction in the estimate o the MRP. At the extreme, the all-inclusive MRP could be set to zero. This implies that the average irm earns a total return equal to the risk-ree rate, 6% in this case. Once again, i γ = 0.5 and T = 30%, about 18% o this return (or 1.1%) is due to ranking credits. I ranking credits are worth about 60% o their ace value 1.1% once distributed, a ranking credit yield o 1.8% is required. This requires a dividend yield 0.6 o 4.12% i all dividends are assumed to be ully ranked. The actual dividend yield in the Australian market is relatively stable at around 4%, but not all o these dividends are ully ranked. Thus, even when the all-inclusive MRP is set to zero, the dividend yield that is required to produce suicient ranking credits to justiy setting gamma to 0.5 is above that which we observe in the market. Moreover, the absence o any sort o risk premium whatsoever is completely implausible so this solution must be rejected. 0 < MRP c 8% Having rejected the case in which the all-inclusive market risk premium is equal to zero, we consider a range o positive values or the market risk-premium beore considering more speciic cases in detail. Historically, Australian excess equity market returns (over and above the yield on 17

18 10-year government bonds) have averaged around 7% p.a. (Dimson, Marsh and Staunton, 2003). Some recent literature which iners the market risk premium rom analyst expectations argues that the market risk premium is less than this historical average. For instance, Claus and Thomas (1999) estimate the market risk premium which is consistent with analyst earnings orecasts and market prices rom They report a mean estimate o 3.4% or the United States and 2.8% or the United Kingdom. Fama and French (2002) estimate the market risk premium at around 3-4% by estimating total returns as the sum o dividend yield and expected growth in dividends or earnings. In addition, Jorion and Goetzmann (1999) contend that survivorship bias makes the historical average equity premium an upwardly-biased estimate o the orward-looking premium. The alternate view is that these eects have already been relected in the 6% estimate that is commonly used in practice. 6 The mean MRP in Australia rom is 7.3%. Thus, an estimate o 6% is already well below the long-term mean. Moreover, there is no evidence o a recent reduction in the MRP. The mean MRP over the last 30 years ( ) is 7.7%. The mean MRP in the 30 year pre-imputation period ( ) is 7.3% and the mean MRP in the postimputation period ( ) is 6.4% 7. In all these cases, MRP is estimated rom dividends and capital gains only. There is no statistical evidence o a reduction in the estimated MRP over time, nor any signiicant dierence in the pre-and post-imputation period. However, appropriate estimation o the MRP is beyond the scope o this paper. We simply attempt to reconcile relative estimates o MRP and gamma with observed dividend yields to highlight any internal inconsistencies. We do this or a range o values or the MRP rom 0 to 8%. For each point in this range, we examine the ull range o values or gamma rom 0 to 1. For each combination o MRP and gamma, we derive the minimum dividend yield that is required to produce the necessary volume o ranking credits. For example, we have shown above that when the MRP is 6% and gamma is 0.5, a ully-ranked dividend yield o 8.2% is required to produce a suicient volume o ranking credits to justiy the 2.1% yield rom ranking credits that is implicit in the other parameter estimates. Figure 2 illustrates the minimum required dividend yield or a range o values or MRP and gamma. 6 Although this value is lower than the available data would suggest, it is consistent with Australian regulatory precedent and market practice as reported in Truong, Partington and Peat (2005). 7 We omit the irst ew years o imputation in line with the conclusion o Brown and Clarke (1993) that the data rom the introduction o imputation in 1987 through 1990 is not representative as the market took some time to adjust to dividend imputation. 18

19 Figure 2: Required minimum ully-ranked dividend yield under alternative assumptions or the market risk premium and the value o ranking credits 18% 16% MRP including ranking credits 8% Required minimum dividend yield 14% 12% 10% 8% 6% 4% 2% 0% Gamma The irst point to note rom this igure is that gamma cannot be set to 0.5 or above. Even when the MRP is set to 0, a ully-ranked dividend yield o at least 4.1% is required to produce the assumed volume o ranking credits. For γ = 0.5 and a MRP o 4%, the ully-ranked dividend yield must be more than 6%. The market simply does not distribute a suicient volume o ranking credits to justiy setting gamma to 0.5. At the other extreme, gamma may be set to 0. In this case, the minimum required dividend yield is, o course, zero. I ranking credits are assumed to have no value to the relevant investor, there is no implicit assumption about how many ranking credits must be distributed and thereore no constraint on the dividend yield. This also applies regardless o the value o the MRP. Thus, setting gamma to zero is consistent with any dividend yield that we observe and with any assumption about the MRP. Now consider an intermediate point. Suppose that we set γ = 0.25 and MRP = 6%. In this case, the total expected return on the market is 12%, o which 1.2% comes rom ranking credits. A ully-ranked dividend yield o 4.5% is required to distribute the required volume o ranking credits in this case. Thus, setting γ = 0.25 and MRP = 6% is reasonably consistent with observed 6% 4% 2% 0% 19

20 dividend yields. What Figure 2 illustrates is that i MRP is set to 6%, the observed dividend yield constrains the value o gamma to 0.25 or less. 8 Similarly, Figure 2 shows that i the MRP is set to only 4%, the maximum value o gamma that can be reasonably entertained, in light o observed dividend yields, is around 0.3. However, this implies that the expected market return is only 10% p.a., o which 1.1% comes rom ranking credits. This implies that dividends and capital gains provide a premium o only 2.9% relative to government bonds, which is so ar at odds with any interpretation o the available data that it could not possibly be considered to be reasonable. In summary, Figure 2 establishes that i gamma is set between 0 and 0.2, any value o the MRP between 0 and 8% is consistent with observed dividend yields. Conversely, i the MRP is set to 6% (consistent with practice), the maximum value o gamma that can be reasonably considered (in light o observed dividend yields) is 0.3. Higher values o gamma can co-exist with lower values o MRP, but on both scores this involves a move away rom the empirical data and market practice. Consequently, we consider this to be nothing more than a theoretical possibility. Higher values o gamma and lower values o MRP are not inconsistent with observed dividend yields, but they are inconsistent with empirical estimates and market practice. T = 75%, MRP c = 6% Consistency with observed dividend yields can be restored i the relevant corporate tax rate is assumed to be 75%, and the 6% estimate o MRP is assumed to include the value o ranking credits. In this case, the average irm earns a total return o 12% p.a., on average. The proportion o this total return that is due to ranking credits is: γ T 1 T ( 1 γ ) = 1 ( 0.5)( 0.75) 0.75( 1 0.5) = 60%. (28) That is, ranking credits yield a return o 7.2%. I ranking credits are worth 60% o their ace 7.2% value once distributed, a ranking credit yield o 12% 0.6 is required. At a tax rate o 75%, T 0.75 ranking credits o $3.00 = can be distributed with every $1.00 o dividends. Thus, 1 T a dividend yield o 4% in line with observed values, would be required. Although consistency 8 Whether these are appropriate values or gamma and MRP is beyond the scope o this paper. That question must be determined with reerence to the available empirical data. The point here is that given the value o one o these parameters, the observed dividend yield constrains the value o the other. 20

21 among parameters, and with observed dividend yields, is restored, a 75% tax rate is completely implausible so this approach must also be rejected. I only a single parameter is to be changed, the only alternative is to set γ = 0. In the remainder o this section, we examine the possibility o simultaneously changing multiple parameters. γ = 0.35, T e = 15%, T stat =30%, MRP dc = 6% The inal approach we examine sets γ = 0.35 and the MRP, excluding ranking credits, to 6%. The latter assumption is consistent with observed data, ater making a downward adjustment to relect an assumed reduction in uture MRP relative to past observations. The value o γ = 0.35 is rom Hathaway and Oicer (2004) 9. We continue to use a statutory tax rate o 30%, which implies 0.3 that 43 cents o ranking credits can be distributed with each dollar o dividends. Finally, we use an eective tax rate o 15%. This suggests that Australian corporate taxes represent 15% o the corporate proits o Australian irms. The most plausible reason or the eective tax rate being lower than the statutory rate is that a portion o the proits are earned oshore and taxed in another jurisdiction. That is, the 15% rate is the proportion o Australian corporate tax (not total tax expense, which may include oreign taxes) to total corporate proit (which does include oreignsourced proits.) However, i this were the only explanation, and i oreign corporate taxes were levied at 30%, hal o all proits o Australian irms would need to be generated oshore. To the extent that the Australian corporate tax rate is relatively high, the proportion o oreign-sourced proits would have to be even higher. Note that this cannot be reconciled by timing dierences (e.g., generous depreciation allowances.) This is because we are dealing with an aggregate o all irms over time. Eventually, timing dierences reverse, such that over a large sample o irms any such dierences would be diversiied away. Finally, note that the total Australian corporate tax paid does represent less than 30% o the total proits o Australian irms. But this statistic is misleading in that minority interests are included in the pre-tax proit o the parent ater tax has been paid by the subsidiary. Suppose, or example, that a subsidiary earns a pre-tax proit o $100, pays $30 corporate tax and distributes a $70 dividend. The 40% owner reports $28 (.4 70) 0 as pre-tax proit and does not subtract 9 Recall that the purpose o the current paper is to examine the consistency o parameter estimates. We do not address the appropriateness o the empirical techniques used to estimate gamma, nor the interpretation o the results. We merely examine whether it is possible to make this reported value consistent with other parameter values and external data on dividend yields. 21

22 corporate tax (as it has already been paid.) Thus, it appears as though some o the proits o the parent have not been taxed, when all corporate proits have actually been taxed when earned. That is, the appearance o a low eective tax rate is a measurement problem and has no economic substance. In a recent analysis, Buini and Fabro (2005) report that the average tax rates o Australia s largest 150 listed irms is %. In summary, the aggregate eective tax rate can only be as low as 15% i large amounts o Australian proits are earned (and taxed) oshore, inconsistent with observed data. This can be considered to be very much a lower bound. Now, i the MRP rom dividends and capital gains is 6%, the adjustment or the value o ranking credits is: MRP c r + MRPdc = r = ( 1 T ) [ 1 T ( 1 γ )] ( ) [ ( ) ] = 6.7%. 6% + 6% 6% (31) Thus, the total required return on the market portolio is 12.7%. O this: γ T 1 T ( 1 γ ) = ( 0.35) ( 0.35) = 5.8%, (32) is due to ranking credits. That is, the return rom ranking credits is 0.74%. I ranking credits are 0.74% worth about 60% once distributed, a ranking credit yield o 1.5% is required. This 0.6 requires a dividend yield o 3.5%, which is broadly consistent with observed yields. The key here is the accelerated distribution o ranking credits they are created by the payment o tax at 15%, but distributed in accordance with the statutory rate o 30%. The advantage o this approach is that the estimate o γ and MRP is based on reported empirical evidence. The assumption o an eective tax rate o 15%, however, is extreme and implies that a very large proportion o Australian corporate proits must be sourced oshore. Conclusions In this section, we have reviewed a number o methods or restoring consistency between parameters and with observed data on dividend yields. Setting γ = 0 is the simplest approach, it completely eliminates all inconsistencies, it is consistent with the most recent published evidence, 22

23 and is consistent with the dominant market practice o corporate inance proessionals and valuation experts. 5. Empirical Adjustments to MRP estimates Some attempts have been made to adjust estimates o the MRP to relect the assumed value o ranking credits. Some details relating to two such approaches have been provided by Australian regulators. Again, we use data rom the regulatory setting because regulators, in contrast to other market participants, provide explicit parameter estimates. The ollowing two examples highlight that, even in the cases where the estimated market risk premium explicitly incorporates an adjustment or ranking credits, that adjustment is inadequate, given the typical assumption that γ = 0.5. To be consistent with observed returns rom dividends and capital gains, either a lower value or γ should be assumed, or a larger adjustment to the MRP is required. In the Review o Gas Access Arrangements Final Decision (2002, p. 324), the Victorian Essential Services Commission (ESC) implicitly notes that there are three components to the equity return: dividends, capital gains and ranking credits. The standard way in which equity returns are measured is in terms o dividends and capital gains only. Thus, the value o ranking credits must be added to any such measure (to the extent that ranking credits have any value to the relevant investor). The ESC reports that (p. 324), its assumption about the value o ranking credits requires an upward adjustment to the measured cash equity premium to add back the non-cash value o ranking credits since 1987 which the Commission has estimated to add 0.2 percentage points onto the long term average. Further calculations indicate that this adjustment was applied by adding around 0.86% to each observation post 1987, thus increasing the average observed MRP rom 1950 by 0.2%. Since this aects 14 o 55 observations, each o those 14 observations must be higher by around 0.86% to cause the average over 55 observations to rise by 0.2%. That is, the ESC values ranking credits as providing a return o around 0.86% p.a. or the average stock (with an equity beta o 1). The Essential Services Commission o South Australia (ESCOSA) (2004, p. 179) has perormed a similar adjustment reporting that, i the non-cash value o ranking credits or the period since 1987 are included the mean MRP over increases by 0.1%. Since this aects 14 o 120 observations, each o those 14 observations must be higher by around 0.86% to cause the average over 120 observations to rise by 0.1%. That is, like the ESC, ESCOSA also values ranking credits as providing a return o around 0.86% p.a. or the average stock (equity beta o 1). Although neither regulator provides any detail about how this 0.86% p.a. return is calculated, it is possible to reverse engineer. The aggregate dividend yield or the Australian market is around 4%. Given that around 10% o dividends are unranked and that very ew dividends are partially 23

24 ranked, the yield o ully ranked dividends is around 3.6% p.a. Since the ratio o ranking credits to dividends is 0.43:1 at a 30% tax rate, the yield o ranking credits is about 1.7% p.a. ( % ) 0. I these ranking credits are valued at around 60% o ace value once distributed 10, they add around 0.86% p.a (.6 1.7% ) 0 to market returns. However, this adjustment is demonstrably inconsistent with the maintained assumptions o γ = 0.5 and T = 30%. To see this, note that i the value o ranking credits is 0.86% and i γ = 0.5, then the total amount o ranking credits created (expressed as a percentage o equity value) must be 0.86% = 1.72%. Since ranking credits are created by the payment o Australian corporate tax, this 0.5 also represents the amount o tax paid. Thus, the average company return beore corporate tax must 1.72% be 5.73%, generating tax o 1.72% and an ater company tax o return o only 4.01%. 0.3 These values are all expressed as a percentage o the equity value. I expressed as a percentage o total irm value, they are even lower! Clearly these implied returns are economically unreasonable. Internal consistency demands that parameters be adjusted as illustrated in Section 4. Setting γ = 0 is the most straightorward adjustment, is consistent with the empirical evidence, and requires no adjustment to market returns whatsoever. The ESC has also sought to adjust its ex-ante estimates o MRP to account or the assumed value o ranking credits. In the Electricity Distribution Price Review Drat Decision (2000, p ), the ESC notes that a grossed-up dividend yield, that includes the assumed value o ranking credits, must be used. This implies that the return to equity-holders is: r D = P ( 1 ) 1 T γ T 1 o e + o g (33) where Do is the current dividend yield and g is the perpetual growth rate o dividends (and earnings P o i the payout ratio is assumed to be constant). As well as applying to individual stocks, this relationship also applies to the market in aggregate. In this case, the dividend yield and growth rate are interpreted as market wide estimates. Using estimate o γ = 0. 5 and T = 30%, and a dividend yield o 4% (consistent with recent data), the expected return on the market portolio is: 10 Recall that the QCA and ESCOSA have explicitly quantiied this value. 24