Stock Performance Analysis and CAPM

The assignment evaluates the performance of Commonwealth Bank (CBA) and Rio Tinto stocks against the All Ordinaries index. It calculates monthly returns, standard deviations, and utilizes the Capital Asset Pricing Model (CAPM) to determine expected returns based on risk-free rates and market risk premiums. The analysis compares actual returns with CAPM predictions, plots the stocks on a security market line (SML), and concludes with an investment recommendation.

ACCOUNTING & FINANCE
omsairam
[Pick the date]

Accounting and Finance
Question 1
(a) Payment per period C=$ 800
Future value of annuity FVA=$ 10,000
Interest rate per period r =10 % p . a.=10
2 %=5 %half yearly
Number of full payments n=?
Size of the concluding payment ¿ ?
Here,
FVA= C∗[ ( 1+r ) n−1 ]
r
10,000= 800∗[ ( 1+0.05 ) n −1 ]
0.05
n= ln1.625
ln1.05 =9.9509
Hence, number of full payment is 9.
Also, the size of concluding payment = 9.9509∗800=$ 7,960.7
(b) Amount invested (initial) would be given as
¿ 200,000−20,000=$ 180,000
Interest (per annum) ¿ 180,000∗10 %=$ 18,000
Interest (for 4 years) ¿ 18000∗4=$ 72,000
Lump-sum amount (at the end of 4 years) ¿ 180,000+72,000=$ 252,000
Present value of annuity PVA= P∗[ 1− ( 1+ r )n ]
r
Where,
P=?
PVA=252000
n=180 months

Accounting and Finance
r =10
12 %=0.833 %
Now,
FV = P∗[ 1− ( 1+ r )−n ]
r
252000= P∗[ 1− ( 1+0.0083 )−180 ]
0.0083
P=252000 /93.43
P=$ 2697.17
Therefore, the monthly payment would be $2697.17.
(c) Payment per year C=$ 4000
Interest rate r =5 % p . a .
Time period n=11 years
Future value of annuity FVA=?
Here,
FVA= C∗[ ( 1+r ) n−1 ]
r
¿ 4000∗[ ( 1+0.05 )11−1 ]
0.05
¿ $ 56,827.15
Dr. Ritz would have $ 56,827.15 in December 2017.
(d) Cash flow for 10 years = $20,000
Time period = 10 years
Discount rate = 6%
Present values of cash flows are given below:

Accounting and Finance
It is apparent that present value of future cash flow is $147,202 which is lower than the
offered amount is $150,000. Therefore, it can be said that Mary Tuna should sell out her
future rights.
(e) Given data
A=$ 1000
r =10 %
i=12 %
n=10 years
Cost of Annuity
P= A ¿
¿ 1000 ¿
¿ $ 8244.26
Question 2
1) It may be assumed that maximisation of profit essentially leads to wealth maximisation for
the shareholders and hence one might be mistaken in assuming both as the same.
However, profit maximisation does not equate to wealth maximisation as the former is
more of a static concept. The concept of profit maximisation does not take into
consideration the underlying risk or time factor and solely focuses on quantum of profits.
This is unlike wealth maximisation which focuses in the future and aims at long lasting
wealth creation. Shareholder wealth may be defined as the present value of all the future
returns that the company would generate through the business (Damodaran, 2010).

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The difference between the two was apparent in the activities being undertaken at the
investment banks before the global financial crisis in 2008. These investment banks were
engaged in highly risky activities which could potentially lead the organisation to bankruptcy.
Such activities may tend to result in profit maximisation but do not lead to wealth creation as
in the long run, loss would result as the focus of the shareholders is not limited to a short
period of time but a longer time period stretching into decades (Brigham and Houston, 2014).
The migration of managerial decision making from shareholder view to stakeholder view is
also driven by a shift from profit maximisation to wealth maximisation. Earlier the managers
were concerned with maximising the profits generated every year due to which such
decisions were taken which led to higher profits in the short term but compromising
reputation or growth of firm over the long run. However, under the stakeholder view,
management aims towards sustainable growth which tends to maximise shareholder wealth
and not necessarily the profits. Hence, ‘maximisation of shareholder wealth’ is a broader and
more imperative concept in comparison with ‘maximisation of profit’ (Arnold, 2005).
2) The risk aversion tends to reflect intolerance towards high risk and corresponding
uncertainty. It is noteworthy that any investment would have atleast a small risk associated
with it and the risk averse investor tends to prefer those investments or financial
instruments that tend to have a lower risk if the choice between two invests offering same
returns has to be made. Further, since risk averse investor does not has appetite for risk,
hence the underlying portfolios and investment projects would have high degree of
certainty with regards to future cash flows (Brealey and Myers, 2007).
An example of risk averse investor can be represented through the use of stock market. A risk
averse investor would look to invest in blue chip companies having low beta which are stable
and would offer decent returns. On the other hand, a risk loving investor would tend to high
beta midcap or small cap stocks which have the potential to deliver stellar returns. However,
it is noteworthy that even for a risk averse investor, there is some degree of risk and the risk
is not zero (Damodaran, 2010).
The same reasoning can be extended to corporate managers where risk aversion would imply
refraining to invest in projects or investments which have high degree of risk. But no matter
in whichever project or investment that the managers go consider to invest in, there would
some degree of uncertainty with relation to future returns and hence risk aversion only
implies investing in projects and investments with low risk and not necessarily zero risk.
Hence, I disagree with the given statement (Lasher, 2007).
Question 3
(i) The relevant data collected from Yahoo Finance is indicated below.

Accounting and Finance
The requisite monthly returns computed are indicated below.
Formula used =[(Monthly closing price – Monthly opening price)/Monthly opening
price]*100
The requisite line chart which indicates the monthly returns for the two stocks and market is
indicated below.

Accounting and Finance
January
February
March
April
May
June
July
August
September
October
November
December
-20.00%
-15.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
Monthly returns in 2016
CBA Rio Tinto All ordinaries index
(ii) The average monthly holding returns are summarised below.
Particulars CBA Rio Tinto All ordinaries index
Average monthly holding period -0.13% 2.87% 0.62%
The above has been computed by taking the average of the various monthly holding period
returns for each of the investment.
(iii) The annual holding period returns can be computed as indicated below.
Opening price on January 4, 2016 (i.e. the first trading day) for CBA = 85.53
Closing price on December 30, 2016 (i.e. the last trading day) for CBA = 82.41
Annual holding period return for CBA = [(82.41-85.53)/85.53]*100 = -3.65%
Opening price on January 4, 2016 (i.e. the first trading day) for Rio = 44.71
Closing price on December 30, 2016 (i.e. the last trading day) for Rio = 59.9
Annual holding period return for Rio = [(59.9-44.71)/59.9]*100 = 33.97%
Opening price on January 4, 2016 (i.e. the first trading day) for All Ordinaries index = 5344.6
Closing price on December 30, 2016 (i.e. the last trading day) for All Ordinaries index =
5719.1

Accounting and Finance
Annual holding period return for All Ordinaries index = [(5719.1- 5344.6)/5344.6]*100 =
7.01%
(iv) The standard deviation of the monthly returns for the two stocks and the market has
been computed using the STDEV function in Excel. The relevant output is as indicated
below.
Particulars CBA Rio
Tinto All ordinaries index
Standard Deviation of monthly returns 6.13% 9.35% 3.52%
(v) The requisite risk return graph is indicated below.
3 4 5 6 7 8 9 10
-10
-5
0
5
10
15
20
25
30
35
40
CBA
Rio Tinto
All ordinaries
index
Risk Return Plot
Risk
Returns (%)
In accordance with the CAPM model, the following is true (Damodaran, 2010).
Expected Returns = Risk free rate + beta *(Expected market returns – Risk free rate)
In the given case, risk free rate = 3.25% and expected market returns – 7%
Hence, expected returns (CBA) = 3.25 + 1.11* (7-3.25) = 7.41% p.a.
Further, expected returns (RIO) = 3.25 + 0.95* (7-3.25) = 6.81% p.a.
(vi) The security market line is shown in the following graph along with the given two
stocks.

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0 0.5 1 1.5 2 2.5 3 3.5
-10
-5
0
5
10
15
20
25
30
35
40
CBA
Rio Tinto
Security Market Line (SML)
Systematic risk
Returns (%)
(vii) It is known that weight of CBA = 60% and weight of Rio = 40%
Hence, portfolio expected returns = wCBA*RCBA + wRIO*RRIO = 0.6*(-3.65) + 0.4*(33.97) =
11.40% p.a.
Portfolio beta = wCBA*βCBA + wRIO*βRIO = 0.6*1.11 +0.4*0.95 = 1.046
(viii) Based on the above analysis, it is apparent that CBA has significantly underperformed
as the return delivered in 2016 is significantly lesser than that expected. However, Rio
Tinto has outperformed the expectations and has managed to generate excess returns for
the shareholders considering the risk return ratio. Also, from the SML and the respective
plotting of the two stocks, it may be highlighted that Rio is immensely undervalued and
CBA is overvalued. Taking the SML along with the CAPM results into consideration, that
one should invest in Rio Tinto stock and not the portfolio or the CBA stock based on the
given information.

Accounting and Finance
References
Arnold, G. (2005) Corporate Financial Management. 3rd edn. Sydney: Financial Times
Management.
Brealey, R., and Myers, S., (2007) Principles of Corporate Finance. 9th edn. New York City:
McGraw –Hill.
Brigham, E. F. and Houston, J. F., (2014) Fundamentals of Financial Management. 14th edn.
Boston: Cengage Learning.
Damodaran, A. (2010) Applied corporate finance: A user’s manual. 3rd edn. New York:
Wiley, John & Sons.
Lasher, W. R., (2007) Practical Financial Management. 5th edn. London: South- Western
College Publisher.