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Lally, Martin --- "Regulation and the Cost of Equity Capital in Australia" [2003] JlLawFinMgmt 3; (2003) 2(1) Journal of Law and Financial Management 15


Regulation and the Cost of Equity Capital in Australia

By Martin Lally[*]

Abstract

This paper examines four issues associated with the Officer model, in the context of estimating the cost of equity capital for regulatory purposes. The conclusions are thus. First, regarding the issue of foreign investors, continued use of a version of the Capital Asset Pricing Model that assumes that national share markets are segmented rather than integrated (such as the Officer model) is recommended. Second, a value for “gamma” of 1 rather than the generally employed figure of .50 is recom mended. Third, in respect of the market risk premium, continued use of the generally employed figure of 6% is recommended. Finally, regarding the differential taxation of capital gains and ordinary income, the simplifying assumption in the Officer model that they are equally taxed could lead to an error in estimating the cost of equity of up to 2% if individual firm values for the dividend yield are used, and up to 1.1% if industry average values are used. Whether this is a sufficiently large sum to warrant concern, and whether the ACCC should lead in this area, are arguable.

1 Introduction

Regulation of the output prices of certain firms is now commonplace in Australia, both at the federal level by the ACCC and at the state level by its counterparts there. In most such cases, a significant element in the determination of these output prices is a fair rate of return on the capital employed. In assessing these fair rates of return, the most significant element is generally the cost of equity capital. In assessing this, the generally employed model is that of Officer[1]. The model is a variant upon the standard form of the Capital Asset Pricing Model (CAPM)[2], to accommodate the presence of Dividend Imputation in Australia[3]. However, like the standard version of the CAPM, it continues to assume that national share markets are completely segregated, and that capital gains and ordinary income are equally taxed.

A number of fundamental questions arise from the use of this Officer approach that are common to the firms examined. The first concerns foreign investors, and the extent to which they should be recognized; the Officer model implicitly ignores such investors by virtue of assuming complete segregation of national share markets. The second question concerns the appropriate value for “gamma” in the Officer model, and its implications for the market risk premium and the effective tax rate. The ACCC currently favours a value of .50[4]. The third question concerns the appropriate value for the market risk premium in the Officer model, with the ACCC (ibid) currently favouring a value of 6%. The final question concerns the simplifying assumption within the Officer model that capital gains and ordinary income are equally taxed. Clearly some investors face lower tax on capital gains than on ordinary income, and this calls into question the Officer assumption.

This paper seeks to address these four issues, with a focus upon the ACCC’s practices[5]. The paper commences with a review of the Officer model, and then examines these four issues in turn.

2 The Officer Model

Officer (op cit) presents a model for the valuation of companies in the presence of Dividend Imputation. The model treats imputation as a process in which some company tax is a prepayment of shareholders’ personal taxation on dividends. The level of company taxation that is treated in this way is the amount assigned as imputation credits, to the extent that investors can use them. The company tax rate is then reduced to refl ect this, and dividends are defined to be the sum of cash paid and the imputation credits, to the extent they can be used. Officer formalizes the model in the context of a level perpetuity, and there is some ambiguity in definitions. However, Monkhouse develops a model that admits any cash fl ow profile and there is less ambiguity in definitions[6]. Two versions are presented, corresponding to each of the two approaches to Imputation that were discussed earlier (as a reduction in company tax or in personal tax on dividends). In respect of the former (Officer) approach, the value of the company is

where Yt is the firm’s year t cash fl ow before deductions for interest and tax, Qt are the year t deductions from Yt to yield taxable income for an unlevered firm, L is the leverage ratio, kd the cost of debt, and the cost of equity with dividends defined to include utilized imputation credits. The effective company tax rate Te is defined as

where Tc is the statutory company tax rate, U a weighted average over investor utilization rates for imputation credits (each investor’s rate can range from zero to 1), IC are the imputation credits assigned by the company during a period and TAX is the company tax paid during that period. The cost of equity, with returns defined to include imputation credits to the extent that they can be used, is

where Rf is the riskfree rate, ße the equity beta defined against the Australian market portfolio, and the expected rate of return on the Australian market portfolio inclusive of imputation credits to the extent they can be used. This is identical to the standard version of the CAPM except that the returns in (3) include imputation credits. If the parameter is expressed as the sum of the conventional expected return km (cash dividends and capital gains), plus the imputation credits to the extent of being usable, then the last equation becomes

where Dm is the cash dividend yield on the market portfolio, and ICm/DIVm is the franking ratio for the market portfolio (the ratio of credits attached to cash dividends paid). Turning now to Officer’s presentation, he introduces the symbol γ (“gamma”), and defines it (op cit, p. 8) such that it must correspond to the following product in (2)

However, he later (op cit, p. 9) uses it in such a way that it must correspond to the utilization rate U. Clearly, if the ratio IC/TAX is equal to 1, then the two uses of “gamma” coincide, and this is consistent with Officer’s consideration of a level perpetuity scenario. However, outside of a level perpetuity scenario, the ratio IC/TAX may be less than 1. The ACCC uses the term to refer to the product in equation (5) rather than the utilization rate[7]. Consistent with this, this paper also uses the term gamma in the sense of (5).

We now consider the valuation formula used by the ACCC[8]. This matches equation (1), except that it values the cash fl ows to equityholders rather than to equityholders and debtholders, i.e.,

where S0 is the value of the cash fl ows to equityholders, Bt is the year t payment to debtholders (principal and interest) and INTt is the year t interest payment. The allowed output price is then chosen (more precisely, an escalation rate applicable to a base level of pricing is chosen) so that the present value of the cash fl ows to equityholders equals the level of equity funding required (being proportion 1-L of the investment required), i.e., defining A as the total investment required, then the escalation rate in the output price is chosen so that

3 The Relevance Of Foreign Investors

Foreign investors are clearly significant in the Australian equity market, with around 30% of foreign shares so held[9]. Furthermore there is virtually free fl ow of equity capital between Australia and the world’s principal equity markets. Prima facie it then seems that models for valuation and the cost of capital should take account of this. However modeling all features of the real world is impossible, and certain abstractions are unavoidable. Inter alia, the Officer version of the CAPM (like the standard version) assumes that national equity markets are completely segregated. As a consequence the “market” portfolio is an Australian one, and betas are defined against it. Versions of the CAPM have been developed that recognize that international investment opportunities are open to investors, starting with that of Solnik[10]. We will examine this model because, dividend imputation aside, it closely parallels the Officer model. As with most international versions of the CAPM, international capital fl ows are assumed to be unrestricted and investors exhibit no irrational home country biases, i.e., there is no preference for local assets for non- financial reasons. Like the standard version of the CAPM, it assumes that interest, dividends and capital gains are equally taxed. The resulting cost of equity for an Australian company is[11]

where Rf is (as before) the Australian riskfree rate, MRPw is the risk premium on the world market portfolio and ßew is the beta of the company’s equity against the world market portfolio. By contrast with the Officer CAPM in equation (4), there is no recognition of dividend imputation. However, since most investors in Australia’s equity market would be foreigners in this full internationalization scenario, and foreigners gain only slight benefits (at most) from imputation credits under any imputation regime, this feature of the model is not significant. The remaining, and significant, distinction between the models lies in the definition of the market portfolio, i.e., the “market” is Australian in the Officer model and the world in the Solnik model. Thus the market risk premiums may differ across the two models and the beta of an asset is defined against a different portfolio.

These distinctions in the market risk premium and beta have significant numerical implications. In respect of the market risk premium, under the Officer model, an estimate of the Australian market risk premium is about 6% (this is discussed in section 6). By contrast, under the Solnik model, in which markets are assumed to be integrated, investors will now be holding a world rather than a national portfolio of equities, and the latter will have a considerably lower variance due to the diversification effect. Since the market risk premium is a reward for bearing risk, then the world market risk premium under integration should be less than that for Australia under segmentation. Stulz argues that, if the ratio of the market risk premium to variance is the same across countries under segmentation, the same ratio will hold at the world level under integration and this fact should be invoked in estimating the world market risk premium[12]. Merton estimates the ratio at 1.9 for the US for the period 1926-78[13]. Harvey offers estimates for 17 countries over the period 1970-90, which average 2.3[14]. All of this suggests a figure of about 2. If we use this figure, then this suggests a market risk premium for the Solnik CAPM of

Cavaglia et al[15] estimates the world market variance over the period 1985-2000 as .1352. Substitution into equation (8) then implies an estimate for the world market risk premium of about .04.

Turning now to the question of betas, the average Australian stock has a beta against the Australian market portfolio of 1, by construction. Similarly, the average asset world-wide has a beta against the world market portfolio of 1, but this does not imply that the average Australian stock has a beta of 1 against the world market portfolio. Ragunathan et al provide beta estimates for a variety of Australian portfolios for the period 1984-1992, against both Australian and world market indexes[16]. The average of the latter to the former is about .40. In addition Gray regresses the Australian index against a world index, for the period 1995-2000, and obtains a beta of .72[17]. The fact that these estimates are less than 1 is unsurprising in view of Australia’s small weight in the world market index and the large weights for some markets. To illustrate this point, suppose the world comprised four equity markets with weights of .01, .245, .245 and .50. Also, the correlation between all markets is .30, and they have the same variance[18]. It follows that the small market (market 1) has a beta against the world portfolio of

regardless of the value for the common variance. The other three markets have betas of .84, .84 and 1.16 (the weighted average of the four betas is of course 1). Lally presents a more realistic example utilizing actual country weights but the outcome is similar: ceteris paribus, very small markets have betas against a world market portfolio that are much less than 1[19]. For illustrative purposes we will assume a beta for a typical Australian stock against the world market portfolio of .70.

We now combine this information about betas and market risk premiums. Employing the Officer CAPM in equation (3), a riskfree rate of .06, and the estimated market risk premium of .06 referred to above, the cost of equity for an average Australian stock would be

ke = .06 + .06 (1) = .12

By contrast, under the Solnik CAPM in equation (7), with the Australian riskfree rate of .06, and estimates for the world market risk premium and the beta of an average Australian stock against the world market portfolio as indicated above, the cost of equity for an average Australian stock would be

ke = .06 + .04 (.70) = .088

The difference in costs of equity under the two models is quite substantial, and is essentially due to the difference in the market portfolio. Since the difference is so large, and the Officer model rests upon an assumption about segregation of national equity markets that is clearly false, then the Solnik model (or some other international CAPM) would appear to be more appealing. However the real test is which is the better description of how the expected returns on equities are determined. All direct tests of this question suffer from the Roll problem, in which the use of mere proxies for the true market portfolio may induce significant test biases[20]. However less direct tests can be performed. One of these is to examine investors’ portfolios. The Solnik CAPM implies that all investors will hold risky assets (both foreign and local) in proportion to their market values. Clearly this is not the case, with investors exhibiting pronounced home country bias, i.e., investors in most major markets hold at least 90% of their risky asset holdings in home country assets[21]. As noted by Huberman, not all international versions of the CAPM have the same implications for investor portfolio holdings, but none can be readily reconciled with this overwhelming home country bias[22].

In view of this significant difficulty, it is understandable that analysts in Australia and elsewhere have not (yet) generally invoked international CAPMs in estimating the cost of equity capital. Furthermore, until home country bias is significantly ameliorated, such caution is likely to persist. A similar caution is warranted in setting the costs of capital for regulated industries. Thus the continued use of a version of the CAPM that assumes that capital markets are completely segregated (such as the Officer model) is recommended.

4 Estimation Of The Utilisation Rate

The utilisation rate is a weighted average across the imputation utilisation rates of investors. This is unclear in Officer (op cit), but is clear from Lally and van Zijl[23]. Furthermore, as indicated in the latter paper, it is a weighted average over all investors in the market rather than those holding the equity in a particular company[24]. One approach to estimating this parameter derives from the fact that the Officer model (like the standard CAPM) assumes that national equity markets are segmented. Consistency then suggests that U be estimated on the basis that all investors in Australian equities are Australians. In respect of such investors, most of those who are taxed can fully benefit from the credits (through a tax rebate for any unutilized credits), whilst tax-exempt investors cannot benefit. Wood estimates that the proportion of shares held by Australians who are tax exempt is 3-4%[25]. Thus the estimate of U should be very close to 1. Even this estimate presumes that tax-exempt investors cannot sell the credits to those who can use them. In so far as they can, the estimate of U should be even closer to 1.

An alternative, and more popular, approach to estimating U is to do so from examination of ex-dividend day returns. Bruckner et al, using data from 1990-93, estimated U as 0.68[26]. The mechanism was as follows: per $1 of cash dividend, the maximum imputation credit attachable with a corporate tax rate (Tc) of .39 was

In addition the average ex-dividend day price drop per $1 of cash dividends was $1.06 for fully franked dividends and 62c for unfranked ones, a difference of 44c. The value U then satisfied the following equation:

This implies that U = 0.68. Other studies yield a range of values: Hathaway and Officer obtain U = 0.44 using 1986-95 data, Brown and Clarke obtain 0.80 using 1989-91 data, and Walker and Partington obtain 0.88 using contemporaneous cum and ex trades in 1995-97[27]. Taking account of these studies, an estimate for U of around .60 is generally employed.

This approach to estimating U is subject to a number of problems. Firstly, the 95% confidence intervals on the estimates are large (for example, Bruckner et al’s is from .44 to .92). Secondly, ex-dividend day returns are known to exhibit perverse behaviour, which contaminates the estimate[28]. Thirdly, these studies assume that capital gains and ordinary income are equally taxed in Australia. This is clearly not the case, and this issue will be examined in more detail in section 7. If capital gains are taxed at 10%, and ordinary income at 30%, then equation (9) becomes

U ($0.64) (1-.30) = $0.44 (1-.10)

and this implies U equals 0.88 rather than 0.68.

Finally, these estimates of U may and presumably do refl ect the presence of foreign investors in the Australian market, who cannot use or fully use the credits and this exerts a downward effect on the estimates[29]. However, as noted earlier, the Officer CAPM (like the standard CAPM) assumes that national equity markets are segmented. Consequently the use of an estimate for U that is potentially significantly infl uenced by the presence of foreign investors introduces an inconsistency into the model. One possible response to this might be to argue that the shortcoming from use of a model that fails to refl ect the reality of international capital fl ows should not be compounded by using an estimate of U that also fails to refl ect international investors. However the effect of recognising foreign investors only in this one respect would be to lower the perceived value of a firm (and hence raise the output price allowed by the ACCC). By contrast, the overall effect of internationalization is likely to involve raising the value of a firm (and hence lower the output price that should be allowed by the ACCC), because the adverse effect upon the usability of imputation credits is likely to be more than offset by the positive effects from a lower risk premium. Thus recognition of foreigners only in the estimate of U would push the calculated value of a firm further away rather than closer to the “correct” answer, i.e., it leads to a raising in the output price allowed by the ACCC when the appropriate direction is a lowering.

To illustrate this point, consider a regulated firm that has just been set up, with no debt, and with assets costing $100m and of indefinite life. The expected output is 1m units per year and there are no operating costs. Letting the allowed output price be denoted P, then the expected cash fl ow in year 1 before company tax is $Pm. Taxable income is likewise and both are expected to grow at 3% pa indefinitely. Consistent with the discussion in the next section, the ratio IC/TAX is assumed to be 1. If equity markets are fully segmented then a utilization rate U of close to 1 will prevail, and we assume 1. In addition the Officer version of the CAPM is employed. Consistent with the example in the previous section, we use a riskfree rate of .06, a market risk premium of .06, and an equity beta of 1, leading to a cost of equity of .12. Following equation (2), the effective tax rate is

Following equation (6), the output price P should be chosen so that the present value of the cash fl ows to equityholders, discounted at the cost of equity of .12, equals the asset cost of $100m, i.e.,

Solving this yields an output price of $9. By contrast, if national equity markets are completely integrated, then the Officer CAPM should be replaced by an international version. Following the discussion in the previous section, we invoke the Solnik model and the estimate there for the cost of equity of this firm of .088. In addition a value for U of zero is appropriate. Recomputing the effective tax rate in (10), and then the output price in (11), the results are

Solving the last equation yields an output price of $8.28. Thus the full effect of internationalization is to reduce the appropriate output price from $9 to $8.28. By contrast, if one continues to use the Officer model but recognizes the effect of internationalization upon the value of U, by reducing the estimate from 1 to the generally employed figure of .60, then the last two equations become

Solving the last equation then yields an output price of $10.23. Thus the full effect of internationalization would be to reduce the allowed output price by 10%, from $9 to $8.28, whereas recognizing only a reduction in U leads to the allowed output price rising by 14% to $10.23. Thus the common practice of recognizing the effect of foreign investors in the estimate of U, but not also in the choice of CAPM, has a totally perverse effect. Accordingly it is not recommended.

In summary then, the estimate for U of around .60 that has been deduced from ex-dividend studies is not recommended. Lonergan[30] goes even further and argues that an appropriate estimate of U is close to zero, primarily because Australia “..is a price-taker in the world’s capital market”[31]. He goes on to note that use of a higher value for U by regulatory authorities leads to the result that “..some investors are being deprived of part of the return to which they properly should be entitled”. However, if it is true that Australia is a price-taker in the world’s capital market, then it follows not only that the value of U is close to zero but also that the appropriate CAPM to employ is an international version. In the above example, the allowed output price should then fall from $9 to $8.28. However, if a value for U of zero was adopted, but the Officer model was still used, then equations (10) and (11) would become

Solving the last equation yields an output price of $12.86. However the correct figure is somewhere between $8.28 and $9. By lowering the utilization rate U, but not also modifying the form of the CAPM, a form of “cherry picking” is being practiced, whose effect is to raise the allowed output price when it should be lowered.

An alternative means of illustrating the same point is to examine a recent ACCC decision in which a WACC is presented that includes within it the imputation effect on company tax. The Moomba Final Decision presents a pre-tax nominal WACC of this form, and the figure given is .09431. Inter alia this calculation embodies a market risk premium of .06, an equity beta of 1.16 and a gamma value of .50 (the product of U and the IC/TAX ratio). If gamma is reduced to zero, as suggested by Lonergan (op cit), then the WACC will rise from .094 to .097, i.e., in the direction recommended by Lonergan. However, consistency requires that an international CAPM is also invoked. Using the Solnik CAPM, with a market risk premium of .04 and an equity beta reduced by 30 percent (as discussed earlier in section 3), the resulting WACC falls to .081, i.e., in the opposite direction to that recommended by Lonergan[32].

In summary then, if the Officer model is used, it is not appropriate to recognize foreign investors in estimating the utilization rate. Consequently an estimate for the latter rate of close to 1 is recommended.

5 Estimation Of The Imputation Credit Ratio

Within the context of the Officer model, the ratio IC/TAX is firm specific. Variation across firms will arise from variation in the ratio of Australian company tax paid to Australian sourced “profits”, and variation in the ratio of cash dividends to “profits”. For example, a firm might generate “profits” of $4m, pay Australian company tax of $1m and pay a dividend of $3m. The maximum imputation credits that can be attached to dividends are the lesser of the tax paid and 43% of the dividend (the latter figure based on the company tax rate of 30%). So the maximum here would be $1m. There is no rationale for withholding imputation credits, and hence this firm would be expected to attach this figure of $1m. The value of IC/TAX would then be 1. However, if the dividend was only $2m, then the maximum imputation credits that could be attached would be $.86m, and therefore IC/TAX would be less than 1.

Within the present context, in which the ACCC prescribes an output price, there are some difficulties in utilizing the firm’s actual ratio IC/TAX. First, it raises the computational burden to the ACCC. Secondly, it generates a further area of controversy in estimation. Finally, in response to this, the firm may be encouraged to manipulate its payout rate. These concerns can be mitigated by using the relevant industry average. This compromise is then recommended.

As an indicator of a typical outcome at the industry level, the ratios for the eight largest listed firms in Australia were examined[33]. In all cases their 2001 financial statements reveal that the ratio IC/TAX was equal to one.

In summary then, it is recommended that the ratio IC/TAX for the firm of interest be set at the industry average. In most cases this should be at or close to one. In conjunction with the recommended estimate for the utilization rate of 1, this implies that the product of these two parameters (gamma) should be at or close to 1 for most firms rather than the ACCC’s currently employed estimate of .50. The effect of this change would be to lower the allowed output prices of regulated firms.

6 Estimation Of The Market Risk Premium

As indicated in equation (4) the market risk premium in the Officer CAPM is defined as

A number of approaches are available for estimating this parameter. The first (following Ibbotson and Sinquefield[34]) employs historical data, and averages over the ex-post annual outcomes for a long time series. The ex-post outcome for (12) in any year is

where Rm is the actual rate of return on the market portfolio over a period, comprising only cash dividends and capital gains. For years prior to 1987, when dividend imputation did not operate, the central term in (13) disappears and the ex-post value is simply Rm - Rf.

In applying the process there are three significant controversies. The first concerns how much historical data is used. Use of older data risks sampling from periods in which the market risk premium was different. However, disregarding all but the most recent data guarantees an impossibly large standard error on the estimate. Theory offers no guidance as to the optimal trade-off.

The second controversy involves whether the time-series averaging should be arithmetic or geometric. Proponents of the latter (minority) view include Copeland et al and Damodaran[35], and Dimson et al show that the effect of using such a process is to reduce the estimate of the Australian market risk premium by almost .02[36]. Cooper[37] argues that, for discounted cash fl ow purposes, one should seek an estimator such that is unbiased with respect to 1 / mn . Because of both the power and inverse transformations just described, an estimator that is unbiased with respect to m will not meet this test. Thus the arithmetic mean is inappropriate. However Cooper offers no support for the geometric mean. The appropriate estimator lies above the arithmetic mean, and hence even further from the geometric mean (which is always below the arithmetic mean). Furthermore, for n < 20 years, the preferred estimator is close to the arithmetic mean. For n > 20 years, the preferred estimator departs significantly from the arithmetic mean but the effect on present value is small. This reasoning assumes that returns are serially independent, and this confl icts with the well-documented evidence of negative autocorrelation in long-horizon returns[38]. However, Indro and Lee show by simulation that negative autocorrelation affects the biases in both arithmetic and geometric means[39]. Nevertheless, for n < 20 years, the effect is very small, so that Cooper’s conclusion is preserved, i.e. the arithmetic mean is a good approximation.

The third significant controversy in this area concerns the choice of term for the riskfree rate. In principle it should correspond to the investor horizon implicit within the CAPM. However the model gives no guidance in determining this. Booth examines the errors that can arise[40]. He shows that the cost of equity will be biased up under the following conditions: the investor horizon is short-term, and the Ibbotson averaging process uses yields on long-term bonds, and the current premium on long-term bonds (p) is higher than the historical average. In addition, even if the current value for p equals the historical average, error will still arise for stocks whose beta differs from 1. It might seem that the solution here is to define the market risk premium relative to short bonds. However, the investor horizon may be long term, and therefore we just swap one source of bias for another.

This Ibbotson methodology is now applied, with arithmetic averaging and long-term (ten year) bond yields. The starting point is Dimson et al (op cit, Table 2), who estimated the Australian market risk premium at .07, using data from 1900-2000[41]. This data omits inclusion of the central term in (12). However, since this term applies only since 1987, the omission exerts only a minor effect on the average across the full 100 years of data. To see this, the May 2002 value for the central term in (12) involves a value for U of 1, a market dividend yield of .032, and a franking rate of .19[42]. The product is .006. If it is attributed to each of the 13 years since the introduction of imputation, the effect upon the estimate of (12) is to raise it by less than .001. In addition to this data issue, the introduction of imputation in 1987 would have introduced a regime shift (downwards) in km. However, as noted by Officer, this should be equal to the central term in (12) so that (12) would have been invariant to the regime shift[43].

A variant on the Ibbotson and Sinquefield (op cit) approach arises from Siegel, who observes that the expected real return on equity appears to be stable over time[44]. This suggests that km should be estimated from the long-run average real return on equity and the current forecast for infl ation. The market risk premium then follows by deducting the current value for the risk free rate, and Siegel generates significantly different results for the US from this approach relative to the Ibbotson approach. This approach is free of the problem identified by Booth (op cit), and described above.

This Siegel approach is applied, as at May 2002, using an average real value of Rm of .091[45], and forecast medium term infl ation of .025[46]. Invoking the Fisher relationship, the resulting estimate for km is then .118. Deducting the long-term bond yield of .062 (using ten year bonds to be consistent with the Dimson et al data[47]) generates an estimate for the market risk premium over long-term bonds of

km – Rf = .118 - .062 = .056

However, as noted, km will have experienced a regime shift downwards with the introduction of imputation, equal to the central term in (12), i.e., UDmICm/DIVm. This regime shift will have had little effect upon the historical average but a more pronounced effect upon the current value. Thus, to estimate the May 2002 value of km, one should deduct the contemporaneous value of the central term from the above estimate of .118. This estimate for km should then be inserted into equation (12), and it yields an estimate for (12) still equal to .056, i.e.,

Amongst other concerns, historical averaging methodology assumes that the true value for the market risk premium has not changed over time. One factor contributing to changes here is changes in market risk, and they have been substantial. Merton (op cit, Table 4) presents US estimates over successive four year periods from 1926 to 1978, and finds that the annuallised standard deviation ranges from .45 during the Great Depression to .11 during the 1960s. This phenomenon has given rise to estimation processes that attempt to model this, starting with Merton, who suggests that the (standard) market risk premium is proportional to volatility. Scruggs[48] clarifies the earlier controversy about the sign of the relationship (French et al and Glosten et al reach opposite conclusions[49]) and concludes that it is positive. However the functional form of the relationship is not apparent. Friend and Blume[50] conclude that aggregate relative risk aversion is constant, and Chan et al[51] show that this implies that the standard market risk premium is proportional to variance.

This methodology is applied to the Australian market, assuming that the market risk premium is proportional to variance. Merton (op cit) estimates the ratio of the standard market risk premium to market variance at 1.9, using US data over the period 1926-78. Harvey (op cit) offers estimates for 17 countries over the period 1970-1990, with a mean of 2.3 and a standard error of .30[52]. All of this suggests a figure of around 2. In addition, Cavaglia et al (op cit) offer an estimate for the Australian market variance over the period 1985-2000 is .183[2]. The resulting estimate of the Australian market risk premium is

2 (.183[2]) = .067

This is an estimate of the standard market risk premium, i.e., km - Rf. If the data used to estimate the reward to risk ratio (estimated at 2) were drawn from the Australian market in the period since imputation was introduced, the estimate of .067 would require addition of the central term in (12). This would raise the .067 figure by about .006, as discussed earlier in this section. If the data were drawn from the Australian market prior to the introduction of imputation, no adjustment would be required because the standard premium in the pre-imputation period should be equal to the Officer premium in the post imputation period. However the data are drawn from a variety of markets, some with imputation and some without. Even in markets with imputation (such as Australia) the data is drawn largely from the pre-imputation period. Thus the figure of .067 requires some adjustment, but by much less than .006. This suggests an estimate for the market risk premium of about .07.

As a form of cross-check upon this reward to risk ratio of 2, application of this methodology to the US market, along with this reward to risk ratio and an estimate of the US market variance over the 1985-2000 period of .1532 (Cavaglia et al, op cit), yields an estimate for the US market risk premium of

2 (.153[2]) = .047

This is remarkably consistent with Cornell’s estimate of .045 by the forward-looking approach[53], or Welch’s result of .045 from survey evidence[54], using long-term bond yields in both cases.

This estimate of the market risk premium is only appropriate for a future period matching that for which current volatility is expected to remain unchanged. For example, if current volatility is expected to remain unchanged only for a short period, then the above estimate of the market risk premium will be appropriate for only that short period. The fact that volatility has changed in the past implies that it will do so in the future. If it follows a random walk without drift, this will not be a concern because today’s value will then be the best estimate for all future years. However, as one might expect, it appears to exhibit mean reversion over time[55]. Consequently one would have to estimate market risk over a sufficiently long period in the past as to act as a good estimate for the future period of interest. For the ACCC’s purpose, in which output prices are set for five years, the estimate for the market risk premium need only hold for five years. Thus an estimate of market volatility should be appropriate for the same period. Just which historical period should be used for this purpose is unclear.

The Merton study is only one of a number of papers that have attempted to generate time-varying estimates of the market risk premium by estimating a functional relationship from historical data. Other examples are Fama and French, Schwert and Pastor and Stambaugh[56]. All appear to face estimation difficulties even more severe than those of the Merton methodology.

All of the above approaches to estimation of the market risk premium utilize historical data. We now, finally, consider “forward-looking” approaches. These approaches first find a value for km that reconciles the current market value of the “market” portfolio with forecasts of future dividends. This is then inserted into equation (12) along with the current values of the other parameters to yield a current estimate of the market risk premium. Thus there is no reliance upon historical data. The mechanics of estimating km are as follows. Let P denote the current value of the “market” portfolio, DIVm the current level of cash dividends and g1, g2.....the forecast growth rates in cash dividends to existing shareholders. It follows that

The focus upon dividends to existing shareholders implies that future share issues can be ignored, and it implies that the expected growth rates g1, g2...are equal to those for dividends per share. From some point (call it year N) the expected growth rate must be assumed to be constant, and is denoted g. Following the constant growth model[57], and letting PN denote the value of the market portfolio in N years, the preceding equation can then be expressed as

where Dm is the current dividend yield on the “market” portfolio. This current dividend yield is observable. However the expected growth rates must be estimated.

A particularly simple case of equation (14) is to assume that the expected growth rates in dividends per share for all future years are equal, i.e., the growth rate g applies immediately and hence N = 0. Equation (14) then collapses to

This is the well known “Discounted Dividends Model” but applied to the entire market rather than a single company. One commonly used approach to the estimation of the expected long-run growth rate in dividends per share (g) is to employ analysts’ forecasts for earnings per share over the next few years[58]. However Cornell (op cit) observes that these shortterm forecasts are typically in excess of reasonable estimates of the long-run growth rate in GDP. Since dividends are part of GDP, the indefinite extrapolation implies that dividends will eventually exceed GDP, and this is logically impossible. Accordingly Cornell suggests that short-run forecasts of the growth rate in earnings per share should converge upon the forecast long-run GDP growth rate, and he suggests a convergence period of 20 years. Since the long-run growth rate in dividends per share (of existing companies) cannot exceed the long-run growth rate in aggregate dividends for all (current and future) companies, and the latter cannot exceed the long-run growth rate in GDP, then the resulting estimate of the market risk premium is an upper bound on the true value.

This Cornell methodology is applied to the Australian market, as of May 2002. Estimates at that time for the weighted average growth in earnings per share of Australian companies were .129 for 2002 and .115 for 2003[59]. In addition the cash dividend yield on the Australian market at that time was .032. Furthermore, an estimate then for the long-run growth in Australia’s GDP was .061, comprising infl ation of .025 and real growth of .035[60].

Using a 20 year convergence period, the expected growth rates in dividends per share are then .129 for the first year, .115 for the second, converging linearly to .061 in year 20, and followed thereafter by .061. Insertion of these expected growth rates into equation (14) then yields an estimate for km of .113. This is then substituted into equation (12), along with May 2002 values for Rf, U, Dm and ICm/DIVm. As indicated earlier in this section, these values are .062, 1, .032 and .19 respectively. This yields an estimate for the market risk premium of

.113 + (1) (.032) (.19) - .062 = .057

This estimate is sensitive to the estimates of the expected growth rates in dividends per share, and these in turn to the long-run real growth rate in GDP (gr) and to the period required before the growth rate in dividends per share converges upon this (N). Some analysts employ only the long-run data, i.e., N = 0[61]. The latter are computationally simple but involve disregarding apparently relevant information (forecasts of earnings per share). Table 1 below shows estimates of the market risk premium as a function of gr and N. In addition to the estimate mentioned above for gr of .035, a lower figure of .030 is also considered, in recognition of the fact that the long run real growth rate in the dividends per share of existing companies must be below the long-run real growth rate in GDP. Plausible values of N are 5-20 years, and this implies an estimate for the market risk premium from .040 to .057.

TABLE 1
Estimated Market Risk Premium
N (yrs)
gr
0
5
10
20
.030
.035
.040
.045
.054
.035
.039
.045
.049
.057

To summarise this review of evidence on the market risk premium in the Officer CAPM, the estimates are .07 from historical averaging of the Ibbotson type, .056 from historical averaging of the Siegel type, .07 from the Merton methodology, and .040-.057 from the forward-looking approach. If a point estimate for the last approach is .048, then the average across these four approaches is .061. In addition various other methodologies have been applied elsewhere, for which Australian results are not available, but which have generated low values in the markets to which they have been employed[62]. All of this suggests that the ACCC’s currently employed estimate of .06 is reasonable.

7 Differential Personal Taxation

As previously discussed the Officer model assumes that ordinary income and capital gains are equally taxed in Australia. The extent to which this assumption is false depends upon the set of investors examined. The principal holders of Australian equities are foreigners, companies, superannuation funds and individuals. As discussed previously in section 4, on account of assuming that national capital markets are segregated, recognition of foreign investors is both inconsistent and leads to perverse results. Accordingly they should be omitted from consideration. In respect of corporate holdings of shares in other companies, inclusion of them would lead to double-counting because the values of shares held by companies is already refl ected in the values of shares held by the other three classes of shareholders. Consequently corporate owners of shares should be ignored. Nevertheless, if companies were subject to taxation on the dividends received from other companies, then the personal tax rates faced by the ultimate recipients of dividends (individuals and superannuation funds) would need to be increased to refl ect this. However, companies are not taxed on dividend income, and therefore this potential complication is absent. Thus, having excluded both foreign investors and corporate shareholders, only individuals and superannuation funds need to be considered.

In respect of individuals and superannuation funds there are three factors that suggest that their taxes on capital gains will be considerably less than on ordinary income. Firstly, it is probable that most of their equities are held for more than one year, and therefore most of the resulting capital gains will be taxed at the concessionary “long-term” rates. This is true despite an average turnover rate for Australian stocks in recent years of around 70%[63], because of wide variation across investors in their holding periods[64]. To illustrate this point, suppose 10% of stock is traded six times a year and the rest is traded every ten years; the turnover rate is then 70% but 90% of stocks are subject to long-term capital gains tax. Secondly, in respect of these long-term gains, individuals are subject to tax on only 50% of the assessable gains, and superannuation funds on only 67% of them[65]. Finally, capital gains are taxed only on realisation and the resulting opportunity to defer payment of the tax is equivalent to a reduction in the statutory rate of tax. Protopapadakis estimates that the opportunity to defer reduces the effective tax rate on capital gains by about 50%[66]. Applying this 50% rate to the preceding figures of 50% and 67% implies that, on average, individual investors and superannuation funds will pay capital gains tax at only 25% and 33% respectively of the rates applicable to ordinary income.

These results suggest that a significant error in estimating the cost of capital may arise from use of a model that assumes equal tax treatment of capital gains and ordinary income. Furthermore the principle that capital gains are taxed less onerously than ordinary income, because of exemptions and/or the deferral option, is well recognised, not only for Australia but other countries including the US and the UK[67]. Within New Zealand this point is sufficiently acknowledged, and has been for several years, to the extent that standard practice in estimating the cost of capital is to invoke a model recognizing less onerous tax treatment of capital gains relative to ordinary income[68].

To determine whether recognition of this issue would materially alter the results from the Officer model, it is necessary to modify the Officer model so as to allow for differential tax treatment of capital gains and ordinary income. Lally and van Zijl have done this and the result is[69]

where D is the cash dividend yield for the company in question. In addition the parameter T is a weighted average (across investors) of the following tax ratio

where ti is the ordinary tax rate of investor i and tgi is their “effective” tax rate on capital gains (i.e., net of the effect of the deferral option). Thus the parameter T is a measure of the extent to which ordinary income is taxed more heavily than capital gains[70]. Lally and van Zijl (ibid) estimate the value of T at .23.

Clearly the formula (15) is more complex than the Officer model (3), and the intuition for the additional terms is as follows. The additional terms are of two types: firstly, a “gross” dividend yield for the firm in question (i.e., inclusive of imputation credits to the extent they are usable), and its market counterpart inside the market risk premium term; secondly, the riskfree rate Rf is replaced by Rf(1-T). In respect of the “gross” dividend yield, as this rises, the firm substitutes gross dividend for capital gain. The former is taxed at the ordinary rate and the latter at the capital gains tax rate. If the ordinary tax rate is higher than the rate on capital gains, then the increase in gross dividend at the expense of capital gain is disadvantageous in tax terms and therefore must be compensated for by higher expected return. This is the effect of the dividend term. In respect of the riskfree rate, to see the effect of this, assume that both beta and the dividend yield are zero. Equation (15) then says that the expected return on equity goes to Rf(1-T), which is less than the riskfree rate. This occurs because the firm’s equity resembles a riskless asset, except that it is taxed as capital gain rather than at the ordinary tax rate applicable to interest. If the tax rate on capital gains is less than the ordinary tax rate (i.e., T is positive) then the expected return of zero beta equity before personal tax does not need to be as high as Rf.

Whether equation (15) yields a materially different result to that of the Officer model (3) depends on a number of factors. Potentially, one of them is how the market risk premium is estimated. One possibility is that the current value of km is estimated by the Siegel (op cit) or forward-looking methods, and then translated into an estimate of the market risk premium using current values of the remaining parameters. In this event, models (3) and (15) will involve the same estimate for km, and hence . The excess of the estimated cost of equity in (15) over that of the Officer model in (3), and denoted Δ , will then be

Clearly the difference here is zero if T is zero, and a sufficient condition for this is that all investors are equally taxed on ordinary income and capital gains. Less apparent, but equally significant, is the fact that the difference will also be zero if the individual company in question matches the market in its beta, dividend yield and franking ratio. By contrast, if the cash dividend yield, beta and the franking ratio for the firm of interest do diverge from the market averages, then Δ may be substantial. Using the values for Rf, U, Dm, ICm/DIVm, and T indicated earlier, of .062, 1, .032, .19 and .23, equation (16) becomes

The bounds on a firm’s dividend yield D are zero to .08 (the latter is the outer limit of observed yields on Australian companies when averaged over the years 1999, 2000 and 2001, and when averages that are significantly infl uenced by one year’s result are excluded). The bounds on the franking rate IC/DIV are zero to .43 (the latter is the largest value possible with a corporate tax rate of .30). Finally, plausible bounds on ße are .50 to 1.50. Using these bounds, the most extreme values for Δ in equation (17) are -.011 and .020.

We now consider the implications of estimating the market risk premium by historical averaging of the Ibbotson type. In this case, one should determine the ex-post value for the market risk premium for each year in a long time-series, and then average over these. As we have indicated earlier, using data for the last 100 years, the result for the Officer model is an estimate of about .07. For the model in (15), and letting AV[ ] denote the sample average over [ ], the estimate would be

The first of these terms is the historical averaging estimate for the market risk premium in the Officer model, i.e., .07. The last term is zero until 1987, because imputation did not commence until then. This represents only 13 of the 100 years in the data used for the historical averaging. Thus an estimate of it is 13% of the average value since 1987. The market cash dividend yield averaged .035 over this period[71]. Thus, even if the franking ratio was as much as .50 and T was as much as .30, then with U = 1, the post 1987 average for the last term in (18) would only be .005. Multiplication by .13 then yields less than .001, i.e., less than .1%. This can be ignored. The average in (18) is then

The last term in (19) is also close to zero because the estimate of T is well below one and, over the last 100 years, the difference between the riskfree rate and the market cash dividend yield has not been large. The average value for Rf over this period was .064[72]. Also, the average for Dm was about .04[73]. If the current estimate for T of .23 is attributed to the last 100 years, then the last term in (19) becomes .005 and the average in (19) becomes .075[74]. The excess of the estimated cost of equity in equation (15) over that of the Officer model in (3) is then

If the firm’s values for D, IC/DIV or ße depart from the market averages, then Δ could be substantial. To demonstrate this we use the values above for Rf, U and T of .062, 1 and .23 respectively. In addition, we use the same bounds used earlier for D, IC/DIV and ße of 0 to .08, 0 to .43 and .50 to 1.50. Accordingly the difference in (20) could range from -.012 to .020.

In summary, the estimated cost of equity from equation (15) could diverge from the Officer model by as much as -.011 to .020 if the market risk premium is estimated through the Siegel or forward-looking methods, and by as much as -.012 to .020 under the Ibbotson estimation method. The results from these two estimation approaches are pleasingly consistent. Clearly an increase in the cost of equity of .020 is significant. However, as indicated in section 5, when discussing the ratio IC/TAX, it may not be desirable to use the firm’s actual values. The compromise suggested there was to use the averages for the relevant industry. Applying the same practice here involves using the relevant industry averages for D and IC/DIV, and this will generate less extreme values for .Δ. For example, if the maximum industry average D (dividend yield) fell from .08 to .053, then the most extreme difference in the costs from equity from models (3) and (15) would fall from .020 to .011[75].

Whether effects up to this level justify a change in the model used is a matter for debate. Clearly no consensus has yet developed amongst Australian academics and practitioners for making such an adjustment, and it is arguable whether the ACCC should lead in this area. Nevertheless, the suggestion that the cost of equity could be increased by up to .011 may lead to some enthusiasm for the adjustment on the part of regulated firms. However the argument for raising the utilization rate on imputation credits from the generally employed figure of .60 to 1 is at least as strong, and will exert a countervailing effect upon the output price granted to a regulated firm. To illustrate this, consider the simple example of a regulated firm in section 4. With a utilization rate on imputation credits of .60 and a cost of equity of .12, the effective tax rate Te and the valuation equation for the firm were as follows

Solving the last equation yielded an output price of $10.23. If the cost of equity is raised by .011, then the last equation becomes

and this implies that the output price rises from $10.23 to $11.48. However, if the utilisation rate is raised to 1, then the effective tax rate falls to zero and the output price then drops back to $10.10, i.e., slightly less than the original $10.23.

8 Conclusions

This paper has examined a series of issues relating to estimation of the cost of equity under the Officer model in a regulatory context. The conclusions are as follows. First, regarding the issue of recognizing foreign investors, continued use of a version of the Capital Asset Pricing Model that assumes that national equity markets are segmented rather than integrated (such as the Officer model) is recommended. It follows that foreign investors must be completely disregarded. Consistent with the disregarding of foreign investors, most investors recognized by the model would then be able to fully utilize imputation credits.

Second, regarding the appropriate adjustment to the company tax rate to refl ect the benefits of imputation, the utilization rate for imputation credits should be set at one, and this follows from the first point above. In addition, the ratio of imputation credits assigned to company tax paid should be set at the relevant industry average, which appears to be at or close to one for most industries. These two recommendations imply that gamma should be at or close to 1 for most companies rather than the generally employed figure of 0.50. The effect of this change would be to reduce the allowed output prices of regulated firms.

Third, in respect of the market risk premium in the Officer model, the range of methodologies examined give rise to a wide range of possible estimates for the market risk premium and these estimates embrace the current value of 6%. Accordingly, continued use of the 6% estimate is recommended.

Finally, regarding the differential taxation of capital gains and ordinary income, the simplifying assumption in the “Officer” model that they are equally taxed at the personal level could lead to an error in the estimated cost of equity of up to 2% if individual firm values for the cash dividend yield and the ratio IC/DIV are used. If industry average values for the cash dividend yield are used, then this maximum figure falls to 1.1%. Arguably this is a sufficiently large sum to justify use of a cost of equity formula that recognizes differential personal taxation of capital gains and ordinary income. However a consensus has not yet developed amongst Australian academics and practitioners for making such an adjustment, and it is arguable whether the ACCC should lead in this area. If such an adjustment were made, it could raise the allowed output prices of some firms. However the argument for raising the utilisation rate on imputation credits is at least as strong, and the net effect of the two changes is unlikely to significantly benefit any firm.

References

[1]. Robert Officer, “The Cost of Capital of a Company Under an Imputation Tax System” (1994), Accounting and Finance 34, pp. 1-17.

[2]. The seminal papers here are William Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (1964), The Journal of Finance 19, pp. 425-42; John Lintner, “The Valuation of Risky Assets and the Selection of Investments in Stock Portfolios and Capital Budgets” (1965), Review of Economics and Statistics 47, pp. 13-37; Jan Mossin, “Equilibrium in a Capital Asset Market” (1966), Econometrica 24, pp. 768-83.

[3]. In doing so the Officer model treats Imputation as a process that lowers the company tax rate and redefines dividends to include the attached imputation credits.An alternative approach is to treat Imputation as a process that lowers the personal tax rate on cash dividends. Examples of the latter approach are as follows: Cheryl Cliffe and Alastair Marsden, “The Effect of Dividend Imputation on Company Financing Decisions and the Cost of Capital in New Zealand” (1992), Pacific Accounting Review 4, pp. 1-30; Martin Lally, “The CAPM Under Dividend Imputation” (1992), Pacific Accounting Review 4, pp. 31-44.The difference in the two approaches is purely a matter of form rather than substance, as shown in Martin Lally, The Cost of Equity Capital and its Estimation (McGraw-Hill Series in Advanced Finance, Volume 3, McGraw-Hill Australia, 2000), pp. 10-11.

[4]. Australian Competition and Consumer Commission, Draft Decision: GasNet Australia Access Arrangement Revisions for the Principal Transmission System (2002).

[5]. The practices of the state regulators generally accord with those of the ACCC.

[6]. Peter Monkhouse, “The Cost of Equity under the Australian Dividend Imputation Tax System” (1993), Accounting and Finance 33, pp. 1-18; Peter Monkhouse, “The Valuation of Projects under the Dividend Imputation Tax System” (1996), Accounting and Finance 36, pp. 185-212.

[7]. Australian Competition and Consumer Commission, Draft Decision: GasNet Australia Access Arrangement Revisions for the Principal Transmission System (2002).

[8]. Australian Competition and Consumer Commission, Access Arrangement by AGL Pipelines(NSW) Pty Ltd for the Central West Pipeline (2000).

[9]. J. B. Were, Australian Equity Market Profile March 1996.

[10]. Bruno Solnik, “An Equilibrium Model of the International Capital Market” (1974), Journal of Economic Theory 8, pp. 500-524.

[11]. This cost of equity is defined in respect of returns that do not include imputation credits, and is therefore denoted as ke without the “hat”.

[12]. Rene Stulz, “The Cost of Capital in Internationally Integrated Markets: The Case of Nestle” (1995), European Financial Management 1, pp. 11-22.It would not be sensible to attempt to estimate the world market risk premium by historical averaging over a long time-series of returns, because even if markets are currently fully integrated this would not have been true for very long.

[13]. Robert Merton, “On Estimating the Expected Return on the Market” (1980), Journal of Financial Economics 8, pp. 323-361.

[14]. Campbell Harvey, “The World Price of Covariance Risk” (1991), The Journal of Finance 46, pp. 111-157, Table VIII.

[15]. Stefano Cavaglia, Christopher Brightman and Michael Aked, “The Increasing Importance of Industry Factors” (2000), Financial Analysts Journal Sept-Oct, pp. 41-54, Table 1.

[16]. Vanitha Ragunathan, Robert Faff and Robert Brooks, “Australian Industry Beta Risk, the Choice of Market Index and Business Cycles” (2001), Applied Financial Economics 10, pp. 49-58, Table 1.

[17]. Stephen Gray, Response to Consultation Paper No. 4: Cost of Capital Financing (2000), submitted to the Office of the Regulator-General Victoria as part of the 2001 Electricity Distribution Price Review.

[18]. The correlation estimate is the average appearing in Patrick Odier and Bruno Solnik, “Lessons for International Asset Allocation” (1993), Financial Analysts Journal March- April, pp. 63-77.

[19]. Martin Lally, “The CAPM under Dividend Imputation and International Capital Markets” (1996), Pacific Accounting Review 8, pp. 48-65, Appendix 2.

[20]. Richard Roll, “A Critique of the Asset Pricing Theory’s Tests: On Past and Potential Testability of the Theory” (1977), Journal of Financial Economics 4, pp. 129-176.

[21]. Ian Cooper and Evi Kaplanis, “Home Bias in Equity Portfolios, Infl ation Hedging and International Capital Market Equilibrium” (1994), The Review of Financial Studies 7, pp. 45-60; Linda Tesar and Ingrid Werner, “Home Bias and High Turnover” (1995), Journal of International Money and Finance 14, pp. 467-492.

[22]. Gur Huberman, “Familiarity Breeds Investment” (2001), The Review of Financial Studies 14, pp. 659-680.

[23]. Martin Lally and Tony van Zijl, “Capital Gains and the Capital Asset Pricing Model” (2003), Accounting and Finance 43, pp. 187-210.

[24]. This averaging is a consequence of aggregating over investors in order to obtain market equilibrium.In intuitive terms the explanation is that market prices are determined by investors in aggregate.

[25]. Justin Wood, “A Simple Model for Pricing Imputation Tax Credits under Australia’s Dividend Imputation Tax System” (1997), Pacific-Basin Finance Journal 5, pp. 465-480, footnote 10.

[26]. Kris Bruckner, Nigel Dews and David White, Capturing Value from Dividend Imputation (1994), McKinsey and Company.

[27]. Neil Hathaway and Robert Officer, “The Value of Imputation Tax Credits” (1995), working paper, University of Melbourne; Philip Brown and Alex Clarke, “The 40 November 2003 Regulation and the Cost of Equity Capital in Australia Ex-Dividend Day Behaviour of Australian Share Prices Before and After Dividend Imputation” (1993), Australian Journal of Management 18, pp. 139-152; Scott Walker and Graham Partington, “The Value of Dividends: Evidence from Cum-Dividend Trading in the Ex-Dividend Period” (1999), Accounting and Finance 39, pp. 275-296.

[28]. Examples are as follows: Murray Frank and Ravi Jagannathan, “Why do Stocks Drop by less than the Value of the Dividend? Evidence from a Country without Taxes” (1998), Journal of Financial Economics 47, pp. 161-188; Philip Brown and Terry Walter, “Ex-Dividend Day Behaviour of Australian Share Prices” (1986), Australian Journal of Management 11, pp. 139-152.

[29]. J. B. Were (see footnote 9) estimate that 30% of Australian equities are foreign owned.This fact alone would point to an estimate for U of .70, which is almost identical to the Bruckner et al estimate (see footnote 26).

[30]. Wayne Lonergan, “The Disappearing Returns” (2001), JASSA Autumn, pp. 8-17.

[31]. Australian Competition and Consumer Commission, Final Decision: Access Arrangement Proposed by Epic Energy South Australia for the Moomba to Adelaide Pipeline System (2001), Table 2.14. The formula used here is formula (7) of Officer (see footnote 1), converted to pretax terms by dividing through WACC by (1-T).

[32]. This issue could also be considered in the context of a CAPM that impounds the imputation tax effect into the discount rate rather than the cash fl ows.The overall effect of a shift from a domestic to an international CAPM is to reduce the discount rate, and this implies a reduction in the allowed output price.This is consistent with the result obtained here.The analysis appears in Martin Lally, “The CAPM with Personal Taxes and International Portfolio Selection” (1998), New Zealand Investment Analyst 19, pp. 22-24.

[33]. These firms were chosen on the basis of market capitalisation as of December 2001, and comprise Telstra, News Corporation, NAB, BHP, Rio Tinto, Westpac, Commonwealth Bank and ANZ.Collectively they represent around 50% of listed equity in Australia.

[34]. Roger Ibbotson and Rex Sinquefield, “Stocks, Bonds, Bills and Infl ation: Year-by-Year Historical Returns (1926-1974)” (1976), Journal of Business, pp. 11-47.

[35]. Tom Copeland, Tim Koller and Jack Murrin, Valuation: Measuring and Managing the Value of Companies (J. Wiley & Sons Inc, New York, 1994), pp. 260-263; Aswath Damodaran, Corporate Finance: Theory and Practice (John Wiley & Sons Inc, New York, 1997), pp. 126-127.

[36]. Elroy Dimson, Paul Marsh and Mike Staunton, “Twelve Centuries of Capital Market Returns” (2000), working paper, Table 5.

[37]. Ian Cooper, “Arithmetic versus Geometric Mean Estimators: Setting Discount Rates for Capital Budgeting” (1996), European Financial Management 2, pp. 157-167.

[38]. See Eugene Fama and Kenneth French, “Permanent and Transitory Components of Stock Prices” (1988), Journal of Political Economy, pp. 246-273; James Poterba and Larry Summers, “Mean Reversion in Stock Prices: Evidence and Implications” (1988), Journal of Financial Economics 22, pp. 27-59.

[39]. Daniel Indro and Wayne Lee, “Biases in Arithmetic and Geometric Averages as Estimates of Long-Run Expected Returns and Risk Premia” (1997), Financial Management 26, pp. 81-90.

[40]. Laurence Booth, “Estimating the Equity Risk Premium and Equity Costs: New Ways of Looking at Old Data” (1999), Bank of America Journal of Applied Corporate Finance 12, pp. 100-112.

[41]. The data are largely drawn from Robert Officer, “Rates of Return to Shares, Bond Yields and Infl ation Rates: An Historical Perspective”, in Share Markets and Portfolio Theory (2nd edition, University of Queensland Press, 1989). However it should be noted that Officer uses bond yields in his calculation whereas Dimson et al (see footnote 36) use bond returns.The use of bond yields seems more in accord with the model and the effect of using them would be to slightly raise the estimate for the market risk premium.

[42]. The data on the dividend yield and franking ratio were courtesy of J P Morgan.

[43]. Robert Officer (see footnote 1), p 10.

[44]. Jeremy Siegel, “The Equity Premium: Stock and Bond Returns Since 1802” (1992), Financial Analysts Journal Jan-Feb, pp. 28-38.

[45]. This data is from Dimson et al (see footnote 36), Table 2.

[46]. This data is from the Australian Department of Treasury, Mid-Year Economic and Fiscal Outlook 2000-01.

[47]. The figure represents an average of the daily rates over April and May.

[48]. John Scruggs, “Resolving the Puzzling Intertemporal Relation Between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach” (1998), The Journal of Finance 53, pp. 575-603.

[49]. Kenneth French, William Schwert and Robert Stambaugh, “Expected Stock Returns and Volatility” (1987), Journal of Financial Economics 19, pp. 13-29; Laurence Glosten, Ravi Jagannathan and David Runkle, “On the Relation between Expected Value and the Volatility of the Nominal Excess Return on Stocks” (1993), The Journal of Finance 48, pp. 1779-1801.

[50]. Irwin Friend and Marshal Blume, “The Demand for Risky Assets” (1975), American Economic Review 65, pp. 900-922.

[51]. K. C. Chan, Andrew Karolyi and Rene Stulz, “Global Financial Markets and the Risk Premium on US Equity” (1992), Journal of Financial Economics 32, pp. 137-167.

[52]. Harvey also gives an estimate for Australia of 1.1, but the standard error of .90 is so large that the estimate is quite unreliable.

[53]. Bradford Cornell, The Equity Risk Premium (John Wiley & Sons, New York, 1999), Chapter 4.

[54]. Ivo Welch, “The Equity Premium Consensus Forecast 41 Journal of Law and Financial Mangement - Volume 2, No. 1 Martin Lally Revisited” (2001), working paper, Yale University.

[55]. Richard Bookstaber and Steven Pomerantz, “An Information-Based Model of Market Volatility” (1989), Financial Analysts Journal Nov-Dec, pp. 37-46.

[56]. Eugene Fama and Kenneth French, “Dividend Yields and Expected Stock Returns” (1988), Journal of Financial Economics 22, pp. 3-25; William Schwert, “Stock Returns and Real Activity: A Century of Evidence” (1990), The Journal of Finance 45, pp. 1237-1257; Lubos Pastor and Robert Stambaugh, “The Equity Premium and Structural Breaks” (2001), The Journal of Finance 56, pp. 1207-1239.

[57]. Myron Gordon and Eli Shapiro, “Capital Equipment Analysis: The Required Rate of Profit” (1956), Management Science 3, pp. 102-110.

[58]. Richard Harris and Felicia Marston, “The Market Risk Premium: Expectational Estimates using Analysts’ Forecasts”, working paper, University of Virginia.Dividends per share may grow at a rate differing from that of earnings per share, by varying the payout rate, but this can only be temporary and must have a future offsetting effect.

[59]. This data was courtesy of J P Morgan.There is evidence of upward bias in analysts’ estimates but the degree appears to be small for forecasts out to two years ahead.For example, an upward bias of less than 1% for this forecast period is reported by James Claus and Jacob Thomas, “The Equity Premium is much Lower than you think it is”, working paper, Columbia University, Table V.Biases of this order would have little effect upon the results in this paper.

[60]. The data are from the Australian Department of Treasury, Mid-Year Economic and Fiscal Outlook 2000-01.By contrast, Cornell (see footnote 53) assumed a long-run real growth rate in GDP for the US of .025.

[61]. An example is Kevin Davis, The Weighted Average Cost of Capital for the Gas Industry (1998), report prepared for the ACCC and the Office of the Regulator-General.

[62]. Ravi Jagannathan, Ellen McGrattan and Anna Scherbina, “The Declining US Equity Premium”, Federal Bank of Minneapolis Quarterly Review 24, pp. 3-19; James Claus and Jacob Thomas, “Equity Premia as low as Three Percent?: Evidence from Analysts’ Earnings Forecasts for Domestic and International Stocks” (2001), The Journal of Finance 56, pp. 1629-1666; Eugene Fama and Kenneth French, “The Equity Premium” (2002), The Journal of Finance 57, pp. 637-659.

[63]. Australian Stock Exchange, ASX Fact File 2002.

[64]. Kenneth Froot, Andre Perold and Jeremy Stein, “Shareholder Trading Practices and Corporate Investment Horizons” (1992), Continental Bank Journal of Applied Corporate Finance, pp. 42-58, Table 1, reveals variations across investor classes in the US ranging from one to seven years, the latter for passive pension funds.The variation across individual investors will be even more pronounced.

[65]. Under the previous tax regime, only the real return was subject to tax.

[66]. Aris Protopapadakis, “Some Indirect Evidence on Effective Capital Gains Taxes” (1983), Journal of Business 56, pp. 127-138.The result refl ects the US tax regime in a period in which long-term capital gains (greater than one year) were subject to concessionary treatment similar to the current situation in Australia.Thus, prima facie, the result is suggestive about the Australian situation.It should also be noted that the opportunity to defer lowers the effective tax rate not only because of the time value of money but also because gains can be realised when the investor’s tax rate is lower, such as in retirement.The latter point is made in Don Hamson and Peter Ziegler, “The Impact of Dividend Imputation on Firms’ Financial Decisions” (1990), Accounting and Finance 30, p 49.

[67]. Peter Howard and Rob Brown, “Dividend Policy and Capital Structure under the Imputation Tax System: Some Clarifying Comments” (1992), Accounting and Finance 32, pp. 51-61; George Constantinides, “Optimal Stock Trading with Personal Taxes: Implications for Prices and the Abnormal January Returns” (1984), Journal of Financial Economics 13, pp. 65-89; David Ashton, “Corporate Financial Policy: American Analytics and UK Taxation” (1991), Journal of Business Finance and Accounting 31, pp. 465-482.

[68]. The New Zealand Treasury, Estimating the Cost of Capital for Crown Entities and State-Owned-Enterprises (1997).

[69]. Martin Lally and Tony van Zijl, “Capital Gains and the Capital Asset Pricing Model” (2003), Accounting and Finance 43, pp. 187-210.

[70]. Equation (15) can also be obtained from a model in which Dividend Imputation is treated as a process that lowers the tax rate on cash dividends rather than the company tax rate.In particular, see Martin Lally, “The CAPM Under Dividend Imputation” (1992), Pacific Accounting Review 4, pp. 31-44; Martin Lally, “Valuation of Companies and Projects Under Differential Personal Taxation” (2000), Pacific-Basin Finance Journal 8, pp. 115-133.The adjustment is to add the imputation credits (to the extent they can be used) to Lally’s formula for the cost of equity.

[71]. Data courtesy of J P Morgan.

[72]. Dimson et al (see footnote 36), Table 2.

[73]. Datastream gives an average of .043 over the period since 1973.

[74]. Clearly the Australian tax regime changes as one moves back through time over the last century. In particular, capital gains tax did not apply to individuals prior to 1986, and this would induce an increase in T. However, it is also true that superannuation funds were not taxed on anything prior to 1986, and this would induce a reduction in T. It is also true that, as one moves back in time, the rates of tax on ordinary income tend to decline, and this also exerts a downward effect upon T. Taking account of all this, the current estimate for T of .23 seems reasonable as an upper bound estimate of the average value over the last 100 years.

[75]. The largest industry average cash dividend yield in 2001 was .053 for “utilities” (data courtesy of J P Morgan).


[*] Associate Professor, School of Economics and Finance, Victoria University of Wellington. This paper is based on “The Cost of Capital Under Dividend Imputation”, 2002, which was prepared for the Australian Competition and Consumer Commission.However, the opinions expressed here, as in the earlier paper, are those of the author.The helpful comments of two anonymous referees are gratefully acknowledged.


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