Equity Valuation

1. EVA 2019 Page 1 of 7
TUTORIAL 8: DISCOUNT RATE
DISCUSSION QUESTIONS
Q1 No, for companies that are included in the index, a 1% change in share price will
have a two- fold effect:- the size of the share price and the weighting of the share
price towards the index, measured as the market capitalisation.
BHP share price is approximately 10 times the price of Amalgamated Holdings and so
other things being equal a 1% change in the share of BHP will have 10 times the
impact on the index. Secondly, the market capitalisation of BHP is approximately 100
times that of Amalgamated Holdings, so that it weighting and therefore 1% change in
share price will be 100 times that of Amalgamated Holdings.
Together, a 1% change in the share price of BHP will have (10 x 100) 1,000 times
more impact on the All Ordinary’s Index than a 1% change in share price of
Amalgamated Holdings.
PROBLEMS
Q1. I have used the following ‘geometric means’ formulas to solve this problem
(1.7) 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝐺𝑟𝑜𝑤𝑡ℎ = (
𝑉𝑎𝑙𝑢𝑒𝑡+𝑛
𝑉𝑎𝑙𝑢𝑒𝑡
)
1
𝑛
⁄
− 1
(1.8) 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝐺𝑟𝑜𝑤𝑡ℎ = [∏ (1 + 𝑟𝑡 )
𝑛
𝑡=1 ]
1
𝑛
⁄
-1
ASX Price
Index
Rf 10 year Rm Rm-Rf
2007 5758 5.94%
2008 3495 6.09% -39.30% -45.39%
2009 3243 5.56% -7.21% -12.77%
2010 3741 5.33% 15.36% 10.03%
2011 3959 5.16% 5.83% 0.67%
Arithmetic average 5.54% -6.33% -11.87%
Geometric mean 5.53% -8.94% -14.47%
ASX
Accum
Rf 10 year Rm Rm-Rf

2. EVA 2019 Page 2 of 7
Index
2007 35345 5.94%
2008 33875 6.09% -4.16% -10.25%
2009 27054 5.56% -20.14% -25.70%
2010 30610 5.33% 13.14% 7.81%
2011 34201 5.16% 11.73% 6.57%
Arithmetic average 5.54% 0.15% -5.39%
Geometric mean 5.53% -0.82% -6.35%
This problem clearly shows (1) geometric mean < arithmetic average (2) returns on
an accumulated index > price index, and (3) It makes no sense to project a negative
return for the risk premium, investors would not enter the market if they expected a
negative return. This suggests the data used here is not appropriate. (4) returns on
the market index is clearly affected by the recent GFC- we expect the returns on a
risky asset to be positive not negative.
Q2. Assume 3 stocks X, Y and Z and index consists of Top 2 stocks by market
capitalisation.
Share price
Period 1 Period 2 Period 3
X $10 $10 $10
Y $1 $1 $1
Z $3 $5 $3
Z declares a dividend of $2 per share and trades ‘cum div’ Period 2 and ‘ex div’
Period 3
Outstanding shares
on issue
X 1,000
Y 20,000
Z 10,000
Period 1
Stock Price Market
Capitalisation
X $10 $10,000
Y 1 20,000
Z 3 30,000
Period 2
Stock Price Market

3. EVA 2019 Page 3 of 7
Capitalisation
X $10 $10,000
Y 1 20,000
Z 5 50,000
Period 3
Stock Price Market
Capitalisation
X $10 $10,000
Y 1 20,000
Z 3 30,000
PRICE INDEX (Top 2 stocks are Y and Z)
Period 1
Stock Weighting Index Value
Y (20/50) .4 ($1) = 0.40
Z (30/50) .6 ($3) = 1.80
2.20 or 220
Period 2
Stock Weighting Index Value
Y (20/70) .286 ($1) = 0.29
Z (50/70) .714 ($5) = 3.57
3.86 or 386
Period 3
Stock Weighting Index Value
Y (20/50) .4 ($1) = 0.40
Z (30/50) .6 ($3) = 1.80
2.20 or 220
Rm
Period 2
Period 3
ACCUMULATION INDEX
Periods 1 and 2 are the same as Price Index
Period 3
Stock Total return Market
Capitalisation
%
76
20
.
2
20
.
2
86
.
3


%
43
86
.
3
86
.
3
20
.
2




4. EVA 2019 Page 4 of 7
X $10 $10,000
Y 1 20,000
Z 5 50,000
Period 3 (Ex div)
Stock Weighting Index Value
Y (20/70) .286 ($1) = 0.29
Z ($2 dividend
added back in)
(50/70) .714 ($5) = 3.57
3.86 or 386
Rm
Period 2
Period 3
Share price index includes a subset of all stocks weighted by each stocks’ market
capitalization (number of shares x share price). Share price indices only captures
capital gain or loss but not dividends paid to shareholders. Accumulation index
makes an adjustment to the share price index to capture dividends that are paid by
stocks included in the index. When measuring returns on share investment, we need
to consider dividend income as well as capital gain/loss. Market returns based on the
accumulation index nullifies the negative impact of dividends measured from the
price index and is therefore preferable since market returns will now resemble the
‘true’ return on a market index and should be used to proxy for the market portfolio
when estimating the risk premium. In Australia return on the accumulation index
tends to be 3-4% higher than on the price index, reflecting the difference in return
attributable to dividends.
Q3. To perform this regression the data should be checked for completeness and
transformed into a returns data set (it makes no sense to regress share prices against
index values). The number of data for CSR is more than that of the index because
data is included for 25 and 26 Dec 2014 which correspond to a public holiday, this is
why the share price has not changed. Therefore the data for these two dates must
be removed so that the size of both data sets is identical (excel will not perform the
task unless this is the case). The output is provided. The Rsquare is 17%, which is
reasonable, but more importantly the pvalue is below 5%, which means it is reliable.
SUMMARY OUTPUT
Regression Statistics
MultipleR 0.413726
R Square 0.171169
Adjusted R Square 0.167854
Standard Error 0.015042
%
76
20
.
2
20
.
2
86
.
3


%
0
86
.
3
86
.
3
86
.
3



5. EVA 2019 Page 5 of 7
Observations 252
ANOVA
df SS MS F
Regression 1 0.011683 0.011683 51.62968
Residual 250 0.056569 0.000226
Total 251 0.068252
Coefficients
Standard
Error t Stat P-value
Intercept 0.000429 0.000949 0.452343 0.651414
X Variable1 0.96668 0.134534 7.185379 7.69E-12
Q4. There is room for variation in answers to this problem. The emphasis for this
problem should be on the methodology issues and selection of appropriate proxies-
emphasis what is reasonable and what is not. Also using excel.
Table 1: Selection the most appropriate measure of beta. In choosing an estimate for
beta, we should be looking as to which measure is most reliable- indicated by the P-
value of variable estimate and Rsq. The P-value is indicator of how reliable the
estimate of the slope (beta) is with a value of 0.05 or less being the most desirable.
The only regressions that do not qualify are the monthly interval for 1, 2 & 3 years
(highlighted in ‘yellow’). The regression with the lowest p-value is daily interval for 4
years (highlighted in ‘green’).
The Rsq tells us how well the variability in the y- variable, returns on CSR’ shares, can
be explained by variation in the x- variable, returns on market index and is an
assessment of both the intercept term and the slope. The regressions with the
highest Rsq value is monthly data measured over the last 12 mths. Since we are
interested in only the coefficient of the x1 variable, the slope, we do not attach as
much importance on the Rsq statistic as the P-value.
Final consideration- more data is better for a reliable estimate ie the central limit
theorem requires data size of 25 – 30 to be considered reliable. This means monthly
data for 1 or 2 years is not preferable to use
Does the fact that CSR underwent asset restructuring in the 2011 financial year alter
your choice?
This may be an important factor since the risk structure of CSR may have changed
post the re-structure. There is a variation in betas going from 3 years to 4 years
which may support this conclusion. The variation in monthly data seems at odds with
the remaining regressions and the low Rsq are consistent with this.
Given the above discussion, the estimate of 1.15 for beta (based on weekly data for
3 years) looks to be the preferred choice.
.

6. EVA 2019 Page 6 of 7
YEARS BETA P-value Intercept R-sq
Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly Daily Weekly Monthly
1 0.964006 1.172923 0.994187 8.89E-12 0.000265 0.071651 0.000502 0.001741 0.009419 0.169611 0.235625 0.288644
2 1.091634 1.012516 0.160308 1.83E-24 1.93E-05 0.665381 0.001244 0.006141 0.031599 0.186597 0.164645 0.00866
3 1.145715 1.151844 0.195375 5.96E-37 2.19E-08 0.573924 0.000973 0.005249 0.027203 0.192219 0.184544 0.009392
4 0.958246 1.013837 0.58067 4.37E-52 2.37E-12 0.044205 0.00038 0.001876 0.010573 0.204593 0.212726 0.086954
Table 2: Choice of risk free rate
Subjective. Govt securities are chosen as a proxy for risk-free rate- NSW govt is regarded as more risky that Federal govt. Choice is between
duration of security (short v long term) and current or average of past rates- there is no ‘right’ answer here except to keep in mind the
influence of the RBA target on interest rates. I have selected the long-term rate- 10 years. I have to be identical with the period over which I
estimate the risk-free rate and the market risk premium because I am trying measure the difference between the two. I have calculated the
geometric average 4.07% (2012 – 2015). There is an argument of selecting a long term security as the duration is similar to shares.
𝐺𝑒𝑜𝑚 𝐺𝑟𝑜𝑤𝑡ℎ 𝑅𝑓 = [(1.03)(1.0323)(1.0354)(1.037)]0.25
− 1 = 3.37%
Table 3: Market risk premium.
The choices here are the type of index, the period over which returns are measured and whether they are measured using geometric or
arithmetic average returns. To be consistent with period over which the risk-free rate is selected and the method of calculating returns I have
chosen the geometric growth rate estimated over the period of 2011 – 2015. Choice of index- it should be accumulation index not price index.
𝐺𝑒𝑜𝑚 𝐺𝑟𝑜𝑤𝑡ℎ (𝐼𝑛𝑑𝑒𝑥) = (
48,602
30,610
)
0.25
− 1 = 12.25%

7. EVA 2019 Page 7 of 7
Note that the Rf for 2011 is not included since the number of data must be identical with Rm. If
I had more data I would have taken a 12 month average for each year, to reduce bias of my
estimate (the value of the index in June for anyone year may not be representative of the
whole year). Therefore the risk premium Rm – Rf = 12.25% - 3.37%= 8.88%. This reasonable but
is probably historically on the high side. Since debt = $0 for 2015, WACC will collapse to the cost
of equity.
Cost of equity = 3.37% + 1.15 (8.88%) = 13.58%
I have taken beta of 1.15 for data measured weekly data over 4 years based on the following
criterion:
1) P-value < 0.05
2) Highest Rsq
3) Data sufficiency (> 25)
4) Economic relevance. CSR has recently undergone re-structuring and therefore a
longer time period is considered more appropriate to reduce the influence of the
most recent data is reduced.
Table 4: Synthetic ratings: Cost of debt
Debt for CSR is not publicly traded (if it was then we could calculate the yield using the bond
formula) and so it needs to be estimated based on either book values or synthetic rates. There
may also be issues with leased assets that are sometimes treated as debt- I have ignored this.
𝐶𝑜𝑠𝑡 𝑜𝑓 𝑑𝑒𝑏𝑡 =
20.7
34.4
= 60.17%
This is unrealistically too high.
Calculation of Interest Coverage ratio for CSR
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑖𝑜 =
𝐸𝐵𝐼𝑇
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒
=
125.5 + 20.7 + 46.2
20.7
=
192.4
20.7
= 9.3
Interest rate on debt = Risk free rate (prevailing interest yield) + Spread
= 3.37% + 1.5% = 4.87%
The original estimate using interest/ book value of debt seems unreasonable, therefore
estimation based on synthetic ratio seems more appropriate.