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GSBS6130 Corporate Finance

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Answer:

Depicting the implied effective annual interest rate:

Particulars

Value

P

$200,000

n

 5 years = 5*12 = 60

A

$232,440

Rate

[P * (1 + i) n]  = A

Rate

(1 + i) 60 = 232440 / 200000

Rate

(1 + i) 60 = 232440 / 200000

Rate

(1 + i) 60 = 1.16

Rate

(1 + i) 60 = 1.0025160

Rate

1 + i = 1.00251

Rate

I = 0.0025 * 60 = 15.05%

 

Particulars

Value

15%

6.665

18%

5.555

15.05%

½(6.665 – 5.555) + 5.555

15.05%, 5

6.11

Exact compounded value

6.11

Depicting the expected life of the winner estimated by Super Lotteries:

Particulars

Value

P

$200,000

r

15.05%

A

$232,440

Time

1-(1+r)-n = r(PV) / P

Time

1- r(PV) / P = (1+r)-n

Time

1- 15.05% *200,000 / 14,148 = (1+15.05%)-n

Time

-1.2755 = (1.15)-n

Time

Log 1.2755 = n Log 1.15

Time

N = Log 1.2755 / Log 1.15

Time

N = 86 years (The supper lottery mainly expects the candidate to live for 86 years.)

Depicting monthly opening and closing price of BKL.AX, MPL.AX and AORD:

 

BKL

MPL

AORD

Date

Open

Close

Open

Close

Open

Close

01-01-16

  217.98

190.57

          2.15

 2.51

   5,344.60

 5,056.60

01-02-16

187.34

158.78

2.52

 2.52

  5,056.60

4,947.90

01-03-16

158.76

177.15

          2.53

 2.93

   4,947.90

5,151.80

01-04-16

177.16

161.00

          2.90

3.14

   5,151.80

5,316.00

02-05-16

162.00

151.20

          3.11

3.20

   5,316.00

5,447.80

01-06-16

 152.50

  131.39

          3.17

 2.95

   5,447.80

5,310.40

01-07-16

 131.50

157.14

          2.97

3.07

   5,310.40

5,644.00

01-08-16

157.65

 123.38

          3.07

2.69

   5,644.00

 5,529.40

01-09-16

123.50

116.58

          2.69

2.48

   5,529.40

5,525.20

03-10-16

117.30

112.08

          2.49

2.58

   5,525.20

 5,402.40

01-11-16

112.00

118.75

          2.56

 2.60

   5,402.40

5,502.40

01-12-16

118.75

103.36

          2.56

 2.82

   5,502.40

 5,719.10

Calculating monthly holding period of BKL.AX, MPL.AX and AORD:

Date

Monthly holding period (BKL)

Monthly holding period(MPL)

Monthly holding period(AORD)

01-01-16

-12.57%

16.74%

-5.39%

01-02-16

-15.25%

0.00%

-2.15%

01-03-16

11.58%

15.81%

4.12%

01-04-16

-9.12%

8.28%

3.19%

02-05-16

-6.67%

2.89%

2.48%

01-06-16

-13.84%

-6.94%

-2.52%

01-07-16

19.50%

3.37%

6.28%

01-08-16

-21.74%

-12.38%

-2.03%

01-09-16

-5.60%

-7.81%

-0.08%

03-10-16

-4.45%

3.61%

-2.22%

01-11-16

6.03%

1.56%

1.85%

01-12-16

-12.96%

10.16%

3.94%

 

Formula for Monthly holding period

(Monthly close price –Monthly open price) / Monthly open price

Monthly holding period

(190.57 – 217.98) / 217.98

Monthly holding period

-27.41 / 217.98

Monthly holding period

-0.1257 or -12.57%

Calculating average monthly holding period returns:

Particulars

Monthly holding period (BKL)

Monthly holding period(MPL)

Monthly holding period(AORD)

Average Monthly holding period

-5.42%

2.94%

0.62%

Depicting annual holding period returns:

Annual holding period

((End Value - Initial Value) / Initial Value + 1 ) ^ ( 1 / Years ) - 1.

BKL

(((((103.36 – 217.98) / 217.98) + 1 ) ^ ( 1 / 1 )) – 1)

BKL

-52.86%

MPL

(((((2.82 – 2.15) / 2.15) + 1 ) ^ ( 1 / 1 )) – 1)

MPL

31.16%

AORD

(((((5719.10 – 5334.60) / 5334.60) + 1 ) ^ ( 1 / 1 )) – 1)

AORD

7.01%

Depicting standard deviation of holding period returns:

Date

Monthly holding period (BKL)

(Monthly holding period – average return)^2

01-01-16

-12.57%

0.51%

01-02-16

-15.25%

0.96%

01-03-16

11.58%

2.89%

01-04-16

-9.12%

0.14%

02-05-16

-6.67%

0.02%

01-06-16

-13.84%

0.71%

01-07-16

19.50%

6.21%

01-08-16

-21.74%

2.66%

01-09-16

-5.60%

0.00%

03-10-16

-4.45%

0.01%

01-11-16

6.03%

1.31%

01-12-16

-12.96%

0.57%

 

Sum

0.159908

 

variance

Sum / (12 -1) = 0.159908 / (11) = 0.014537

 

SD

√ 0.014537 = 0.12056984

 

Date

Monthly holding period (MPL)

(Monthly holding period – average return)^2

01-01-16

16.74%

1.91%

01-02-16

0.00%

0.09%

01-03-16

15.81%

1.66%

01-04-16

8.28%

0.28%

02-05-16

2.89%

0.00%

01-06-16

-6.94%

0.98%

01-07-16

3.37%

0.00%

01-08-16

-12.38%

2.35%

01-09-16

-7.81%

1.16%

03-10-16

3.61%

0.00%

01-11-16

1.56%

0.02%

01-12-16

10.16%

0.52%

 

Sum

       0.089567

 

variance

Sum / (12 -1) = 0.089567 / (11) = 0.008142

 

SD

√ 0.008142 = 0.09023551

 

Date

Monthly holding period (AORD)

(Monthly holding period – average return)^2

01-01-16

-5.39%

0.36%

01-02-16

-2.15%

0.08%

01-03-16

4.12%

0.12%

01-04-16

3.19%

0.07%

02-05-16

2.48%

0.03%

01-06-16

-2.52%

0.10%

01-07-16

6.28%

0.32%

01-08-16

-2.03%

0.07%

01-09-16

-0.08%

0.00%

03-10-16

-2.22%

0.08%

01-11-16

1.85%

0.02%

01-12-16

3.94%

0.11%

 

Sum

       0.013613

 

variance

Sum / (12 -1) = 0.013613  / (11) = 0.001238

 

SD

√ 0.001238 = 0.03517825

Calculating covariance of BKL & MPL, BKL & Market, and MPL & Market over the year:

Date

(Monthly holding period – average return)^2 (BKL)

(Monthly holding period – average return)^2 (MPL)

BKL * MPL

01-01-16

-7.15%

13.80%

-0.987%

01-02-16

-9.82%

-2.94%

0.289%

01-03-16

17.01%

12.87%

2.189%

01-04-16

-3.70%

5.33%

-0.197%

02-05-16

-1.24%

-0.05%

0.001%

01-06-16

-8.42%

-9.88%

0.832%

01-07-16

24.92%

0.43%

0.106%

01-08-16

-16.31%

-15.32%

2.499%

01-09-16

-0.18%

-10.75%

0.019%

03-10-16

0.97%

0.67%

0.007%

01-11-16

11.45%

-1.38%

-0.158%

01-12-16

-7.54%

7.21%

-0.544%

 

 

Sum

0.0406

 

Covariance

Sum / (12 -1) = 0.0406 / (11) = 0.0036866

 

Date

(Monthly holding period – average return)^2 (BKL)

(Monthly holding period – average return)^2 (AORD)

BKL * AORD

01-01-16

-7.15%

-6.01%

0.42980%

01-02-16

-9.82%

-2.77%

0.27224%

01-03-16

17.01%

3.50%

0.59502%

01-04-16

-3.70%

2.56%

-0.09483%

02-05-16

-1.24%

1.86%

-0.02307%

01-06-16

-8.42%

-3.14%

0.26472%

01-07-16

24.92%

5.66%

1.41051%

01-08-16

-16.31%

-2.65%

0.43279%

01-09-16

-0.18%

-0.70%

0.00125%

03-10-16

0.97%

-2.85%

-0.02772%

01-11-16

11.45%

1.23%

0.14069%

01-12-16

-7.54%

3.32%

-0.24987%

 

 

Sum

0.0315

 

Covariance

Sum / (12 -1) = 0.0315 / (11) = 0.0028650

 

Date

(Monthly holding period – average return)^2 (MPL)

(Monthly holding period – average return)^2 (AORD)

MPL * AORD

01-01-16

13.80%

-6.01%

-0.82968%

01-02-16

-2.94%

-2.77%

0.08155%

01-03-16

12.87%

3.50%

0.45021%

01-04-16

5.33%

2.56%

0.13681%

02-05-16

-0.05%

1.86%

-0.00089%

01-06-16

-9.88%

-3.14%

0.31074%

01-07-16

0.43%

5.66%

0.02407%

01-08-16

-15.32%

-2.65%

0.40642%

01-09-16

-10.75%

-0.70%

0.07507%

03-10-16

0.67%

-2.85%

-0.01914%

01-11-16

-1.38%

1.23%

-0.01694%

01-12-16

7.21%

3.32%

0.23922%

 

 

Sum

0.0086

 

Covariance

Sum / (12 -1) = 0.0086 / (11) = 0.0007795

Calculating the expected portfolio return and standard deviation for 40% of wealth is invested in BKL and 60% in MPL:

 

Weight

Expected return

Standard deviation

BKL

40%

-5.42%

0.120569837

MPL

60%

2.94%

0.090235512

Portfolio Expected return

(40%*-5.42%) + (60%*2.94%) = -0.40%

Portfolio Standard deviation

    (40%*-0.120569837) + (60%*0.090235512) = 0.1024

Calculating the expected portfolio return and standard deviation for 10% of wealth is invested in BKL and 90% in MPL

 

Weight

Expected return

Standard deviation

BKL

10%

-5.42%

0.120569837

MPL

90%

2.94%

0.090235512

Portfolio Expected return

(10%*-5.42%) + (90%*2.94%) = 2.11%

Portfolio Standard deviation

    (10%*-0.120569837) + (90%*0.090235512) = 0.093

Calculating beta of the both BKL and MPL:

Beta

Cov(BKL, AORD) / (Variance AORD)

Beta

0.0028650 / 0.001238

Beta of BKL

2.31515

 

Beta

Cov(BKL, AORD) / (Variance AORD)

Beta

0.0007795 / 0.001238

Beta of MPL

0.62988

Expected return according to CAPM of BKL and MPL:

CAPM = Rf + Beta * (Rm – Rf)

Rf

2.75%

 

Rm

7.01%

 

 

CAPM Return

Beta

BKL

2.75% + 2.31515 * (7.01%-2.75%) = 12.61%

2.31515

MPL

2.75% + 0.62988 * (7.01%-2.75%) = 5.43%

0.62988

AORD

7.01%

1

Rf

0.0275

0

k. Constructing SML showing BKL, MKT and MPL:

Being rational investors investment in MPL could be identified as the most viable options because it is has lower risk and provides adequate return within the market expected return. The rational investor would not opt for BKL investment, as it has the highest risk, which increases risk chances of loss from investment. Barberis, Greenwood, Jin & Shleifer (2015) mentioned that CAPM model mainly uses the risk evaluation method to determine the minimum expected return from an investment. On the other hand, Habibi, Habibi & Habibi (2016) criticises that CAPM model mainly lose its friction, as it does not depicts the current valuation condition of the shares of a company, which could increase chances of huge loss.

Reference and Bibliography:

Barberis, N., Greenwood, R., Jin, L., & Shleifer, A. (2015). X-CAPM: An extrapolative capital asset pricing model. Journal of Financial Economics, 115(1), 1-24.

Habibi, H., Habibi, R., & Habibi, H. (2016). Derivation of Kalman Filter Estimates Using Bayesian Theory: Application in Time Varying Beta CAPM Model. Journal of Statistical and Econometric Methods, 5(2), 1-16.

Jagric, T., Podobnik, B., Strasek, S., & Jagric, V. (2015). Risk-adjusted performance of mutual funds: some tests. South-eastern Europe journal of Economics, 5(2).

Lipiec, J. (2014). Capital Asset Pricing Model Testing at Warsaw Stock Exchange: Are Family Businesses the Remedy for Economic Recessions?. International Journal of Financial Studies, 2(3), 266-279.

Mazzola, P., & Gerace, D. (2015). A Comparison Between a Dynamic and Static Approach to Asset Management Using CAPM Models on the Australian Securities Market. Australasian Accounting Business & Finance Journal, 9(2), 43.

Strachinaru, A. I., Gutu, L. M., & Ilie, V. (2014). Stock Market Model in Romanian Pharmaceutical Sector. International Journal of Trade, Economics and Finance, 5(1), 126.

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