Cost of Equity Calculation Methods

This assignment delves into the calculation of the cost of equity using different multifactor models. It explores the three-factor and five-factor Fama-French models, which enhance upon CAPM by incorporating additional risk factors. The discussion also includes the Arbitrage model, which integrates macroeconomic variables. The objective is to understand how these complex models provide a more reliable estimation of the cost of equity compared to simpler approaches like the Gordon Dividend model and CAPM.

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BHP, CBA & WOW
STUDENT ID:
[Pick the date]

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a) The three companies that are selected for this task are as follows.
 BHP Billiton Limited
 Commonwealth Bank of Australia
 Woolworths Limited
The dividend payment history for the above three stocks has been obtained from DatAnalysis
Premium database for the time period starting on July 1, 2007 and ending on June 30, 2017.
The dividend payment history is highlighted in the table indicated below.
b) In order to compute the dividends paid for each company on an annual basis, the interim
dividend would need to be annualised as 6 month of interest would be received taking into
consideration an applicable rate of interest as 2.72% p.a. The relevant formula and
approach for annualising an interim dividend is indicated below.
Annualised dividend = Interim Dividend *(1+ 0.0272)0.5
In the above formula, the time period is six months or 0.5 years.
Based on the above formula, the annual dividend for the last ten years for the selected
stocks is summarised in a tabular manner indicated below.

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c) The growth rate of dividend for the three selected companies has been summarised in the
table highlighted below based on which the average dividend growth rate has been
computed.
Based on the average dividend growth rate during the period, it is apparent that for
Woolworths, the average dividend growth rate is way too low which is being adversely
impacted due to the significant drop in dividend in FY2016. For BHP Billiton, the average
dividend growth rate seems way too high which is attributed to the abnormal jump in FY2017
which is an aberration rather than being the normal trend. However, for CBA or
Commonwealth Bank, the average dividend growth represents a realistic value which would
be used as a proxy growth rate for dividend.
For BHP Billiton, there was a severe drop in dividend in FY2016 owing to the loss that the
company had made. Further, the high growth in dividend in FY2017 is also attributed to the
dip in dividends in FY2016. Hence, these two values would be excluded from the average
dividend growth rate computation. Further, years FY2009 and FY2015 are also not being

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considered since these years saw a significant shift in the commodity prices. Based on the
remaining years i.e. FY2010 –FY2014, the average dividend growth rate comes out as 8.29%
p.a. which would act as the proxy dividend growth rate.
For the computation of proxy dividend growth rate for Woolworths, the last two years i.e.
FY2017 and FY2016 growth estimates would be ignored as due to the sudden decline in
dividends in FY2016, the average is being impacted adversely. Also, in FY2017, the dividend
growth rate may be exaggerated due to the lower base value in FY2016. Hence, the proxy
rate would be the average dividend growth rate for the period FY2009-FY2015 which comes
out to be 6.19% p.a.
Next year dividend (BHP Billiton) = (83.54/100)(1+0.0829) = $0.9047
Next year dividend (CBA) = (431.59/100)(1+0.0627) = $ 4.588
Next year dividend (Woolworths) = (84.46/100) (1+0.0619) = $ 0.897
d) Based on the closing prices on June 30, 2017 and the above estimates of next year
dividend and also proxy dividend growth, using Gordon dividend model, the cost of equity
would be computed for the three selected stocks.
BHP Billiton
Closing price as on June 30, 3017 = $ 23.28
Applying the Gordon dividend model and the relevant information, we get
23.28 = 0.9047/(k-0.0829)
Solving the above, k = 0.1218 or 12.18% p.a.
The cost of equity for BHP Billiton is quite reasonable considering that in mining sector,
when the commodity prices are firm, the profitability margins are quite high. Further, BHP
Billiton has a market leadership position as it is one of the largest mining companies with
mines located in various geographies. Also, considering the fluctuations in commodity prices
on a periodic basis, the risk tend to be higher thus leading to higher expectations in terms of
returns.

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CBA or Commonwealth Bank of Australia
Closing price as on June 30, 3017 = $ 82.81
Applying the Gordon dividend model and the relevant information, we get
82.81 = 4.588/(k-0.0627)
Solving the above, k = 0.1181 or 11.81% p.a.
The cost of equity seems reasonable considering the risky nature of industry especially after
the financial crisis. Further, it is likely that the credit card fee based earnings may be
adversely impacted as government introduces strict regulations to prevent abuse on the part
of banks. Additionally, there may be burst of property bubble which may lead to default on
home loans and the same may not be recovered from sale of property causing losses to the
banking sector (Creighton, 2017). However, considering that CBA is one of the four major
banks in the banking space in Australia, thus, the bank is expected to escape any such crisis.
But considering the current state of banking industry, the cost of equity is reasonable to
expect.
Woolworths Limited
Closing price as on June 30, 3017 = $ 25.54
Applying the Gordon dividend model and the relevant information, we get
25.54 = 0.897/(k-0.0619)
Solving the above, k = 0.0970 or 9.70% p.a.
The above rate of equity is pretty low considering the outlook of the company and the sector.
Currently, the sector is facing cutthroat competition as the various discount retailers such as
Aldi are trying to penetrate the market. Further, in the recent years there has been a sizable
drop in market share of Woolworths which is a matter of concern. Also, the company is
facing difficulties while trying to cope with discount retailers such as Costco (Berry, 2016).
Hence, there is higher risk associated with investment in this stock and sector for which there
needs to be higher returns for the investor that the current computed cost of equity. Therefore,
it may be concluded that the actual cost of equity would be higher than the estimated value.

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e) Even though the Gordon dividend model is quite popular, but there are a host of
methodological issues inherent in the application of this model. One of the key issues with
the use of Gordon discount model is to determine the intrinsic value of those stocks which do
not pay dividend. There are typically high growth companies where the management needs to
deploy the profits into future growth of the company rather than giving dividend income to
the shareholders. Since the basic premise of Gordon model is that the value of the share is
essentially the present value of all future dividends, thus the model fails in evaluating the
value of such stocks (Brigham and Ehrhardt, 2013). One solution that is used for such
companies is to use the EPS instead of dividend taking into consideration that Modigliani
Miller model about dividend not being relevant is true. However, the use of EPS further gives
rise to another methodological issue which is to determine the EPS growth rate going forward
which is difficult considering that EPS tends to be more volatile in comparison with
dividends (Petty et. al., 2015).
Another issue with the methodology of Gordon’s approach is based on the assumption that
the steady state growth can never exceed the equity cost. Clearly, there is no theoretical or
empirical basis for this assumption and hence in certain cases where the dividend growth rate
tends to exceed the cost of equity, this model cannot be used (Christensen et. al., 2013). Yet
another issue in the application of the model deals with the constant growth rate. Typically,
firms tend to follow a life cycle and a constant growth rate of dividend is only achieved only
when the firm attains a maturity. However, for other firms assuming a constant dividend
growth rate is clearly inappropriate. In order to accommodate such firms, a multi stage
dividend model is applied. But despite the use of such a model, the determination of the
constant dividend growth rate remains an issue (Damodaran, 2008). This problem is further
compounded from the fact that the intrinsic price of the stock is highly sensitive to the growth
rate and thus error in the same could potentially lead to disastrous conclusions. As a result,
the reliability of the model remains low particularly for companies which have not entered
the maturity phase as only in this phase a reasonable estimation of the dividend growth can be
made based on the empirical behaviour of the company in this regard (Graham and Smart,
2012).
Considering the shortcomings of the dividend growth model particularly with regards to
application, other models have been proposed which aim to estimate the cost of equity. One
of the most common alternatives in this regards is the CAPM approach or Capital Asset
Pricing Model. The basic equation of this model is indicated below.

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E(R) = Rf + β(RM – Rf)
In the above equation, E(R) essentially captures the cost of equity or the returns that the
investor expects from the share of a given firm. Rf is the risk free rate where RM is the market
return which is derived based on the historic trends. Further, the systematic risk which is
associated with a given stock is captured by the respective beta (Brealey, Myers and Allen,
2008).
The basis of the above model lies in the fact that the investor who tends to invest in the stock
market tends to assume risk for which he/she needs to be compensated in the form of higher
returns or else any investor would not assume incremental risk. As a result, the expected
return on the stock is directly proportional to the beta or systematic risk of the stock
computed relative to the market index (Graham and Smart, 2012). Hence, for assuming
incremental risk, the investor is being compensated by providing incremental returns. Even
though this model seems theoretically sound along with easy to use, but there is a plethora of
criticisms that various scholars and practitioners have lined up against this approach
(Christensen et. al., 2013).
One of the key issues with CAPM is the set of unrealistic assumptions on which it is based.
This is because the assumptions considered are not satisfied by the security markets. A
particular assumption is in relation to the homogeneous expectations of the investors which
apparently is false as these are typically driven from the underlying objectives and risk
appetite that the given investor has (Guerard, 2013). Besides, CAPM also assumes that
investors tend to take rational decision and thereby tensd to ignore the impact of emotions on
human decision making particualrly in relation to investment. The empirical studies which
have taken place tend to reflect on the key role that human emotions along with various
biases play while the investor takes decisions and hence there are instances where rationale
takes a backseat (Northington, 2013). Additional assumption that is made for CAPM is that
information is available free of cost and hence everyone can access the same. But even in the
current day security markets, information carries a premium and trades are initiated based on
information that a particular investor has while the other lacks the same. Yet one more
assumption on which CAPM is based is that the money lending and borrowing is carried out
at risk free rate which is clearly incorrect as the respective rates charged from each investor
would be driven by the underlying creditworthiness and default risk (Damodaran, 2008).

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Thus, the above discussion clearly indicates that CAPM approach tends to be driven by
unrealistic assumptions.
Another major criticism of the CAPM approach relates to the inability of beta as a measure of
risk. During the last two three decades, using historical data from various developed markets,
a host of research has been carried to validate the model but most of these studies have found
that the historical returns observed do not satisfy the CAPM model (Parrino and Kidwell,
2011). An additional criticism that is levelled against CAPM is that it is based on historical
data which has limited relevance for the future and hence would lead to conclusions that are
not relevant and reliable (Petty et. al., 2015). Thus, the discussion on CAPM clearly
highlights that while this model is comparatively more user friendly than Gordon dividend
but the set of assumptions and use of historical data and beta tend to raise questions. As a
result, this alternative is not much superior to the Gordon dividend approach (Marcus and
Kane, 2013).
An alternative approach which aims to rectify the shortcoming associated with using beta
alone as a measure of risk is in the form of multi factor models which have been given by
Fama and French based on their research regarding the CAPM and improving on the model
so as to ensure that the historical data tends to verify the model. There are two variants of
Fama French model one is three factor model and the other is the five factor model. These
models tend to work on a similar theoretical framework as CAPM but tend to capture risk in
a more reliable manner (Brealey, Myers and Allen, 2008). Another approach which is based
on the usage of multiple factors is the Arbitrage model which tends to introduce various
macroeconomic variables as factors influencing the cost of equity. Further, with the
tremendous enhancement in the computing power, these complex models are gaining more
acceptance in comparison to the rather simplistic approaches as suggested by Gordon model
and CAPM approach (Damodaran, 2008). The objective is to build on these models and
ensure that the cost of equity can be computed with more reliability. Thus, the multifactor
models tend to act as better alternatives to both the Gordon dividend and also the CAPM
approach.

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References
Berry, P. (2016), Woolies appears to be losing its battle with Aldi and Coles over the $11
billion groceries market, News Website, [Online] Available at
http://www.news.com.au/finance/business/retail/woolies-appears-to-be-losing-its-battle-with-
aldi-and-coles-over-the-11-billion-groceries-market/news-story/
ee619afcd95cab694d1a40687fef869c [Accessed September 3, 2017]
Brealey, R, Myers, S and Allen, F (2008), Principles of Corporate Finance, 9th edn., New
York: McGraw Hill Publications
Brigham, EF and Ehrhardt, MC (2013). Financial Management: Theory & Practice, 14th
edn., New York: South-Western College Publications
Christensen, M, Drew, M, Blanchi, R and Ross, S (2013), Fundamentals of Corporate
Finance, 6th edn., New York: McGraw Hill
Creighton, A. (2017), If the housing bubble bursts economy will come tumbling down, The
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creighton/if-the-housing-bubble-bursts-economy-will-come-tumbling-down/news-story/
3012c2eb2dd2264d27dd8c3ff201925b [Accessed September 3, 2017]
Damodaran, A. (2008), Corporate Finance, 2nd edn, London: Wiley Publications
Graham, J. and Smart, S. (2012), Introduction to corporate finance, 5th edn. Sydney: South-
Western Cengage Learning,
Guerard, J. (2013), Introduction to financial forecasting in investment analysis, 6th edn., New
York: Springer
Marcus, A.J. and Kane, B.Z. (2013), Essentials of Investment, 9th edn, Singapore: McGraw-
Hill International
Northington, S. (2011), Finance, 6th edn., New York: Ferguson
Parrino, R & Kidwell, D (2011), Fundamentals of Corporate Finance, 3rd edn., London:
Wiley Publications,

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Petty, JW, Titman, S, Keown, AJ, Martin, P, Martin JD and Burrow, M (2015), Financial
Management: Principles and Applications, 6th edn, Sydney: Pearson Australia