Calculation of annual returns:
|
Month |
Apple Ltd |
Returns |
Month |
Orange Ltd |
Returns |
Month |
Market Index |
Returns |
|
Share price ($) |
Share price ($) |
(ASX index) |
||||||
|
Jan-16 |
13.05 |
0.00% |
Jan-16 |
20.55 |
0.00% |
Jan-16 |
4650 |
0.00% |
|
Feb-16 |
13.4 |
2.68% |
Feb-16 |
21.15 |
2.92% |
Feb-16 |
4770 |
2.58% |
|
Mar-16 |
13.87 |
3.51% |
Mar-16 |
20.95 |
-0.95% |
Mar-16 |
4840 |
1.47% |
|
Apr-16 |
13.12 |
-5.41% |
Apr-16 |
18.75 |
-10.50% |
Apr-16 |
4940 |
2.07% |
|
May-16 |
13.37 |
1.91% |
May-16 |
17.1 |
-8.80% |
May-16 |
4815 |
-2.53% |
|
Jun-16 |
13 |
-2.77% |
Jun-16 |
19.35 |
13.16% |
Jun-16 |
4788 |
-0.56% |
|
Jul-16 |
13.5 |
3.85% |
Jul-16 |
20.1 |
3.88% |
Jul-16 |
5055 |
5.58% |
|
Aug-16 |
13.9 |
2.96% |
Aug-16 |
21.05 |
4.73% |
Aug-16 |
5125 |
1.38% |
|
Sep-16 |
14.12 |
1.58% |
Sep-16 |
22.15 |
5.23% |
Sep-16 |
5035 |
-1.76% |
|
Oct-16 |
14.87 |
5.31% |
Oct-16 |
23.85 |
7.67% |
Oct-16 |
5115 |
1.59% |
|
Nov-16 |
15.25 |
2.56% |
Nov-16 |
22.9 |
-3.98% |
Nov-16 |
5200 |
1.66% |
|
Dec-16 |
16.05 |
5.25% |
Dec-16 |
21.85 |
-4.59% |
Dec-16 |
5255 |
1.06% |
|
Jan-17 |
16.4 |
2.18% |
Jan-17 |
23.8 |
8.92% |
Jan-17 |
5305 |
0.95% |
|
Annual return |
23.61% |
Annual return |
17.69% |
Annual return |
13.49% |
(Source: Appendix A) (Source: Appendix A) (Source: Appendix A)
Comment:
It is seen that annual return of Apple ltd and annual return of orange ltd are more than market index annual return. Further it is also seen that Apple ltd annual return is more that Orange ltd which shows that both companies are performing well according to market index but Apple ltd is performing best among the three (Fama, 1990).
Calculation of standard deviations:
|
Month |
Apple Ltd |
Returns |
Month |
Orange Ltd |
Returns |
Month |
M Market Index |
Returns |
|
Share price ($) |
Share price ($) |
(ASX index) |
||||||
|
Jan-16 |
13.05 |
0.00% |
Jan-16 |
20.55 |
0.00% |
Jan-16 |
4650 |
0.00% |
|
Feb-16 |
13.4 |
2.68% |
Feb-16 |
21.15 |
2.92% |
Feb-16 |
4770 |
2.58% |
|
Mar-16 |
13.87 |
3.51% |
Mar-16 |
20.95 |
-0.95% |
Mar-16 |
4840 |
1.47% |
|
Apr-16 |
13.12 |
-5.41% |
Apr-16 |
18.75 |
-10.50% |
Apr-16 |
4940 |
2.07% |
|
May-16 |
13.37 |
1.91% |
May-16 |
17.1 |
-8.80% |
May-16 |
4815 |
-2.53% |
|
Jun-16 |
13 |
-2.77% |
Jun-16 |
19.35 |
13.16% |
Jun-16 |
4788 |
-0.56% |
|
Jul-16 |
13.5 |
3.85% |
Jul-16 |
20.1 |
3.88% |
Jul-16 |
5055 |
5.58% |
|
Aug-16 |
13.9 |
2.96% |
Aug-16 |
21.05 |
4.73% |
Aug-16 |
5125 |
1.38% |
|
Sep-16 |
14.12 |
1.58% |
Sep-16 |
22.15 |
5.23% |
Sep-16 |
5035 |
-1.76% |
|
Oct-16 |
14.87 |
5.31% |
Oct-16 |
23.85 |
7.67% |
Oct-16 |
5115 |
1.59% |
|
Nov-16 |
15.25 |
2.56% |
Nov-16 |
22.9 |
-3.98% |
Nov-16 |
5200 |
1.66% |
|
Dec-16 |
16.05 |
5.25% |
Dec-16 |
21.85 |
-4.59% |
Dec-16 |
5255 |
1.06% |
|
Jan-17 |
16.4 |
2.18% |
Jan-17 |
23.8 |
8.92% |
Jan-17 |
5305 |
0.95% |
|
Standard Deviation |
3.03% |
Standard Deviation |
6.99% |
Standard Deviation |
2.03% |
|
Annualized standard deviation |
10.93% |
|
Annualized standard deviation |
25.20% |
|
Annualized standard deviation |
7.30% |
(Source: Appendix A) (Source: Appendix A) (Source: Appendix A)
|
Comparing the annualized standard deviation of two companies it is seen that Apple ltd standard deviation is 10.93% whereas standard deviation of Orange ltd is 25.20% which means Apple ltd has least risk a compare to Orange Ltd. |
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Further it is also seen that market index has least standard deviation as compare to both companies. This is because standard deviation of market comprises of standard deviation of companies listed in that particular market and forms an average risk taking all companies risks comprises in that market (Tsiang, 1972). |
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|
Question4
Calculations of Beta:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Beta of Apple |
0.1471 |
Beta of a stock measures the volatility of the stock with repect to market index. If beta value of a stock is more than one then it is referred as ‘high beta stock’ means this types of stock are riskier than market index whereas if beta value of a stock is less than one then it is referred as ‘low beta stock’ this means stocks under this category are not riskier than market index (Babcock, 1972).
Here the beta of Apple ltd and orange ltd are less risky than market index. But comparing the beta of these two companies it can be said beta with high are more risky than beta with low value. Hence, Apple ltd has more risk than Orange Ltd.
|
Beta of Orange |
0.0157 |
|
Given information: |
|
|
|
Companies |
Beta [calculated in Q4] |
Weights [given] |
|
Apple Ltd |
0.147071207 |
40% |
|
Orange Ltd |
0.015665314 |
60% |
|
Calculation of Portfolio Beta: |
|
|
|
|
|
|
Portfolio beta = Weights of Apple * beta of apple + weights of orange * beta of orange |
|||||
|
Bp |
0.068227671 |
Comment:
|
Portfolio beta is the combined beta of all stocks according to the proportion of investments. |
|
Here the Portfolio beta is smaller than apple ltd whereas it is bigger than orange ltd (Markowitz, 1991). |
Calculation of Risk free rate (Rf):
|
Rf (%) |
5.39 |
(Source: Appendix D)
Calculation of Expected returns of Apple Ltd and Orange Ltd as per CAPM model:
Ri = Rf + β(Rm-Rf)
(Bruner, et.el., 2008).
Where,
|
Rf (%) |
5.39 |
|
Rm (%) [calculated in Q1] |
13.49 |
|
Apple ltd |
|
Orange Ltd |
||
|
Beta |
0.147071207 |
|
Beta |
0.015665314 |
|
Ri (%) |
6.58 |
|
Ri (%) |
5.52 |
|
Given information: |
|
|
|
Bond information |
Apple Ltd |
Orange Ltd |
|
Maturity value (FV) |
150000 |
200000 |
|
Current price |
140000 |
215000 |
|
Coupon rate |
9% |
10% |
|
Time to maturity |
6 years |
5 years |
|
Suppose, face value of bond |
100000 |
|
|
Given that interest paid semiannually. For calculation of YTM, time gets doubled and interest rate gets half. |
|
YTM = C + (FV -CP)/n |
|
Particulars |
Apple ltd |
Orange ltd |
|
YTM = Yield to maturity |
||
|
C = Interest amount |
4500 |
5000 |
|
FV = fair Value |
150000 |
200000 |
|
CP = current price |
140000 |
215000 |
|
n = no. of years |
12 |
10 |
|
Apple Ltd |
|
|
|
YTM (annually) |
7.36% |
|
|
Orange Ltd |
|
|
|
YTM (annually) |
3.37% |
|
(Rode.et el, 1976)
|
Given Information: |
|
|
|
|
|
Apple Ltd |
|
Orange Ltd |
||
|
Debt |
50% |
|
Debt |
30% |
|
Equity |
50% |
|
Equity |
70% |
|
Ke [calculated in Q6] |
6.58% |
|
Ke [calculated in Q6] |
5.52% |
|
WACC = Weight of Debt * Kd + Weight of Equity * Ke |
|||
|
|
Apple Ltd |
Orange Ltd |
|
|
Weight of debt |
50% |
30% |
|
|
Kd |
0 |
0 |
|
|
Weight of equity |
50% |
70% |
|
|
Ke |
6.58% |
5.52% |
|
|
WACC |
3.29% |
3.86% |
WACC is very useful for investors because it represents minimum rate of return. In other words, WACC is the overall cost of capital of the company which comprises of different category of capital is proportionately weighted. It includes common stock, debts, preferred stock. Thus, WACC of orange ltd is higher than WACC of Apple ltd which indicates investors should invest money in Orange ltd (Farber, Gillet and Szafarz, 2006).
Calculation of growth rate as per CAGR method:
|
|
Apple Ltd |
Orange Ltd |
|
Growth rate (g) |
4.56% |
5.92% |
(Source: Appendix B)
|
Given Information: |
|
|
|
Particulars |
Apple Ltd |
Orange Ltd |
|
Ke [calculated in Q6] |
6.58% |
5.52% |
|
Growth rate (g)[calculated in Q9] |
4.56% |
5.92% |
|
Dividend of current year [2015] |
1.25 |
2 |
(Source: Appendix B)
Calculation of market value of shares as per dividend discount model:
|
DDM = Dividend of current year/(Ke – g) |
||
|
|
|
|
|
|
Apple Ltd |
Orange Ltd |
|
market value of share ($) |
62.00 |
-497.0 |
|
Comment: |
|
|
|
|
|
|
|
Value of Apple is $ 62 whereas value of orange is in negative but taken as Zero. |
(Penman, 1998).
Penman, S.H., 1998, ‘a synthesis of equity valuation techniques and the terminal value calculation for the dividend discount model’, A review of accounting studies, vol.2, no.4, pp.303-323.
Rode, F., Crowley, Jr, W.L., Walker, A.D. and Cochran, D.S., Hewlett-Packard company, 1976, general purpose calculator with capability for performing yield-to-maturity of a bond calculation, U.S.
Markowitz, H.M., 1991, ‘foundation of portfolio theory’, the journal of finance, vol.46, no.2, pp.469-477.
Fama, E.F., 1990, ‘stock returns, expected returns, and real activity’, the journal of finance, vol.45, no.4, pp.1089-1108.
Tsiang, S.C., 1972, ‘the rationale of the mean-standard deviation analysis, skewness preference and the demand for money’, the American economic review,vol.62, no.3, pp.354-371.
Babcock, G.C., 1972, ‘a note on justifying beta as a measure of risk’, the journal of finance, vol.27, no.3, pp.699-702.
Bruner, R.F., Li,W., Kritzman, M., Myrgren, S. and Page, S., 2008, ‘market integration in developed and emerging markets: evidence from the CAPM’, Emerging markets review, vol.9, no.2, pp.89-103.
Farber, A., Gillet, R.L. and Szafarz, A., 2006, a general formula for the WACC.
Lettau, M and Ludvigson, S.C., 2005, ‘expected returns and expected dividend growth’, Journal of financial Economics, vol.76, no.3, pp.583-626.
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