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Questions:

Answer the following assignment questions. Provide comments or explanation where required and provide literature support for your explanation with proper in-text citation and references.

1.Calculate the annual returns for Apple Ltd, Orange Ltd and the Market using the information provided in Appendix A. Compare the annual returns of the market and 2 companies and comment.

2.Calculate the standard deviations of the returns of the Market and 2 companies.

3.Annualise the standard deviations of the Market and two companies. Compare annualised standard deviations of two companies and the Market. Do you see annualised standard deviation of the market is smaller than two companies' annualised standard deviation? If so, explain why?

4.Calculate the beta for both companies. Using the concept of the Beta as a 'measure of risk'. Comment on the riskiness of both companies.

5.You have decided to have a portfolio of Apple Ltd and Orange Ltd. Your portfolio consists of 40% of Apple Ltd shares and 60% of Orange Ltd shares. Calculate the Portfolio beta. Is portfolio beta is smaller or bigger that individual company beta? Explain your answer.

6.Calculate the required rate of return for both companies using the Capital Asset Pricing Model (CAPM). Use the information provided in Appendix D to calculate the risk free rate.

7.Calculate the Yield to Maturity (bond's market rate) for the both companies' using the information given in Appendix C.

8.Calculate the Weighted average cost of capital (WACC) of both companies assuming that Apple Ltd's capital structure consists of 50% debt and 50% equity whereas Orange Ltd's capital structure is made up of 30% debt and 70% equity. Compare their WACCs and comment.

9.Calculate the growth rate for both Apple Ltd and Orange Ltd using Compound Annual Growth Rate (CAGR) using the information provided in Appendix B.

10.Calculate the Market value of the share of both companies using the Dividend Discount Model. Compare the share prices of two companies and comment.
Answers:
Question1

 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).

Question2 and 3

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%

Calculation of annualized standard deviations:

Annualized standard deviation

10.93%

 

Annualized standard deviation

25.20%

 

Annualized standard deviation

7.30%

(Source: Appendix A) (Source: Appendix A) (Source: Appendix A)

Comment:

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).

Question4

Calculations of Beta:

Mar-16

13.87

3.51%

4840

1.47%

 

 

Mar-16

20.95

-0.95%

4840

1.47%

Apr-16

13.12

-5.41%

4940

2.07%

 

 

Apr-16

18.75

-10.50%

4940

2.07%

May-16

13.37

1.91%

4815

-2.53%

 

 

May-16

17.1

-8.80%

4815

-2.53%

Jun-16

13

-2.77%

4788

-0.56%

 

 

Jun-16

19.35

13.16%

4788

-0.56%

Jul-16

13.5

3.85%

5055

5.58%

 

 

Jul-16

20.1

3.88%

5055

5.58%

Aug-16

13.9

2.96%

5125

1.38%

 

 

Aug-16

21.05

4.73%

5125

1.38%

Sep-16

14.12

1.58%

5035

-1.76%

 

 

Sep-16

22.15

5.23%

5035

-1.76%

Oct-16

14.87

5.31%

5115

1.59%

 

 

Oct-16

23.85

7.67%

5115

1.59%

Nov-16

15.25

2.56%

5200

1.66%

 

 

Nov-16

22.9

-3.98%

5200

1.66%

 

Beta of Apple

0.1471

Comment:

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.

Question5

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).

Question6

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

Question7

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.

Calculation of YTM of Apple ltd and Orange Ltd

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)

Question8

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%

Calculation of WACC of Apple ltd and orange ltd:

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%

 
Comment:

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).

Question9

Calculation of growth rate as per CAGR method:

 

Apple Ltd

Orange Ltd

Growth rate (g)

4.56%

5.92%

(Source: Appendix B)

Question10

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).

References

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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