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Question 1

1.(a).Whenever an asset is added to a portfolio, the total risk of the portfolio will be reduced provided the returns of the asset and the portfolio are less than perfectly correlated. Discuss. (200 words approx.)

(b).Minco Ltd, a large mining company, provides a superannuation fund for its employees. The fund’s manager says: ‘We know the mining industry well, so we feel comfortable investing most of the fund in a portfolio of mining company shares’. Advise Minco’s employees on whether to endorse the fund’s investment policy.  (approx. 200 words)

(c).Harry Jones has invested one-third of his funds in Share 1 and two-thirds of his funds in Share 2. His assessment of each investment is as follows:

Share 1

Share 2

Expected return

15%

21%

Standard deviation

18%

25%

Correlation between the returns

0.5


a) What are the expected return and the standard deviation of return on Harry’s portfolio?

b) Recalculate the expected return and the standard deviation of return on Harry’s portfolio where the correlation between the returns is 0.

c) Recalculate the expected return and the standard deviation of return on Harry’s portfolio where the correlation between the returns is 1.0.

d) Is Harry better or worse off as a result of investing in two securities rather than in one security?

2.(a).Why are bond prices and yields inversely related? Doesn’t a higher yield make a bond more attractive to investors and hence make it worth more, not less? (

(b).Differences between the current yields on different bonds can be explained by their relative riskiness and different terms to maturity. Discuss. 

(c).Jeremy Kohn is planning to invest in a $1,000 10-year bond that pays a 12 percent coupon. The current market rate for similar bonds is 9 percent. Assume semi-annual coupon payments. What is the maximum price that should be paid for this bond?

(d).Shawna Carter wants to invest her recent bonus in a $1,000 four-year bond that pays a coupon of 11 percent semi-annually. The bonds are selling at $962.13 today. If she buys this bond and holds it to maturity, what would be her yield?

(e) .Jorge Cabrera paid $980 for a $1,000 15-year bond 10 years ago. The bond pays a coupon of 10 percent semi-annually. Today, the bond is priced at $1,054.36. If he sold the bond today, what would be his realised yield?

3.(a).The valuation of a share using the dividend growth model is very sensitive to the forecast of the dividend growth rate. This feature is a serious limitation on its usefulness to a share analyst. Discuss. 

(b).The required rate of return on the shares in the companies identified in (a) to (c) below is 15 per cent per annum. Calculate the current share price in each case.

  1. a) The current earnings per share of Zero Ltd are $1.50. The company does not reinvest any of its earnings, which are expected to remain constant.
  2. b) Speedy Ltd’s current dividend per share is 80 cents. This dividend is expected to grow at 5 per cent per annum.
  3. c) Reduction Ltd’s current dividend per share is 60 cents. The dividend of the company has been growing at 12 per cent per annum in recent years, a rate expected to be maintained for a further 3 years. It is expected that the growth rate will then decline to 5 per cent per annum and remain at that level indefinitely.

(c).Pioneer Ltd’s preference shares are selling for $33 each and pay a $3.60 annual dividend.

(a) What is the expected rate of return on a preference share?

(b) If a preference share investor’s required rate of return is 10% p.a., what does the value of the preference share for the investor? (c) Should the investor purchase Pioneer Ltd’s preference shares?

(d).Stag Company will pay dividends of $4.75, $5.25, $5.75, and $7 for the next four years. Thereafter, the company expects its growth rate to be at a constant rate of 7 percent. If the required rate of return is 15 percent, what is the current market price of the share?

Question 1

1.a) A portfolio of strong diversification can be attained when the investment is done in less than positively correlated investments. This is due to the fact that when the asset is added to the portfolio it will create opportunities where the change in one variable will bring change in another variable. Thereby, the total risk will be reduced and an opportunity of enhanced return will occur. Both the assets and the portfolio must be less than perfectly correlated that means introduction of the asset will bring change in the value of the asset and vice versa. When less than positively correlated there is a chance of less risk as the investment pattern is not linked to individual assets. Therefore, less than positively correlated will bring better returns. A diversified portfolio can be attained when there is a presence of uncorrelated assets however, such is subjected to risk (Davies & Crawford, 2012).  Hence, the concept of less than positively correlated will work in this scenario as it will lead to better result. Overall, the reduction of the risk in a portfolio can be attained by having asset in the portfolio with characteristic of less than perfectly correlated.

(b)

Yes, the employees can endorse the fund’s investment policy as the superannuation fund is handled by the manager and decision is taken after due consideration of the employees.  If the employees will endorse the fund investment policy it will create a better situation as the other employees will be able to know about the policy. Moreover, an investment into the mining industry will fetch good result because the manager is confident of that and aims to enhance the returns. Endorsing the fund’s investment policy will create awareness and will tend to bring a more rational approach (Graham & Smart, 2012). This will ultimately provide support to the management and helps in framing a better policy. Moreover, endorsing the policy will send positivity to the management and hence, the manager can have better opportunities in the future. However, before the endorsement, the employees need to have better outlook of the investment that will help them in chalking out the entire investment and to be well-versed with all the pros and cons of the policy.

a)

Share 1

Share 2

Expected return

15%

21%

Standard deviation

18%

25%

Correlation between the returns

0.5

Weights

33.33%

66.67%

Share Name

Returns

Weights

Portfolio Return

Share 1

15%

33.33%

5.00%

Share 2

21%

66.67%

14.00%

19.00%

Portfolio Return

=

19.00%

Covariance of portfolio

=

(0.50 x 18% x 25%)

=

0.0225

Standard deviation of portfolio

=

((1/3)^2 (18%)^2 + (2/3)^2 (25%)^2 + 2 (1/3) (2/3) (0.0225))^(1/2)

=

20.34%

b)

Share 1

Share 2

Expected return

15%

21%

Standard deviation

18%

25%

Correlation between the returns

0

Weights

33.33%

66.67%

Share Name

Returns

Weights

Portfolio Return

Share 1

15%

33.33%

5.00%

Share 2

21%

66.67%

14.00%

19.00%

Portfolio Return

=

19.00%

Covariance of portfolio

=

(0 x 18% x 25%)

=

0

Standard deviation of portfolio

=

((1/3)^2 (18%)^2 + (2/3)^2 (25%)^2 + 2 (1/3) (2/3) (0))^(1/2)

=

17.71%


c)

Share 1

Share 2

Expected return

15%

21%

Standard deviation

18%

25%

Correlation between the returns

1

Weights

33.33%

66.67%

Share Name

Returns

Weights

Portfolio Return

Share 1

15%

33.33%

5.00%

Share 2

21%

66.67%

14.00%

19.00%

Portfolio Return

=

19.00%

Covariance of portfolio

=

(1 x 18% x 25%)

=

0.045

Standard deviation of portfolio

=

((1/3)^2 (18%)^2 + (2/3)^2 (25%)^2 + 2 (1/3) (2/3) (0.045))^(1/2)

=

22.67%


d)

Portfolio diversification is always considered useful to reduce the risk of loss. Investing in two securities helps him reduce his overall risk. Investing in two securities is not enough if the securities correlation coefficient is near to 1. It is said that higher the risk, higher the return. Whether Harry is better off and worse off, depends on his expectation. If he prefers to avoid risk, he is better off. On the contrary, if he prefers higher risk for getting a return, he is worse off.

2.(a)

When the issue of bonds takes place then it carried a coupon rate or a rate that is near to the prevailing market interest rate. As a matter of fact yields and prices of bonds have an inverse relationship therefore when one surge ahead the other falls. This happens because investors are always comparing their current investments and what they can get from the market rate. As the interest rate of the market undergoes a change which is fixed becomes less attractive to the investors and hence they ate willing to pay more or less for the same bond (Parrino et. al, 2012).

a) Risk reduction in a portfolio

When it comes to high-yield bonds they are investments of high risk and for this specific reason, they have the strong scope of providing higher returns as compared to others. Moreover, prices of high yield bond are sensitive in nature and a change in the financial outlook will change the interest rate (Choi & Meek, 2011).  Therefore, going by the pattern it can be said that a higher yield bond will be more attractive to the investors as compared with a lower yield.

(b)

The maturity and the riskiness of the bonds determine the current yield. The level of risk that a bond contains is reflected by the pattern of return. This is called the current yield and is a function of the coupon rate and the current price. The coupon rate is termed as the interest rate per annum that the issue needs to provide to the investor and is even termed as a percentage of the par value. Moreover, the current yield of the bond must be higher so that it can compensate for a higher level of risk (Horngren, 2013). If the market considers the current yield of the bond is low the price will fall to bring that yield to the same level in tune to the expectation of the market or as per the rate of interest rate that is prevailing in nature

(c)

Face Value

=

1000

Interest rate on bond

=

12%

Semi-annual interest payment

=

1000 x 12% x (1/2)

=

60

Semi-annual Market rate

=

9% / 2

=

4.50%

Number of interest payments

=

10 x 2

=

                     20

Current price of bond

=

(1000 / (1 + 4.5%)^20)  + ( (60 / 4.5%) (1 - (1 + 4.5%)^(-20)))

=

         1,195.12

(d)

Face Value

=

1000

Interest rate on bond

=

11%

Semi-annual interest payment

=

1000 x 11% x (1/2)

=

55

Number of interest payments

=

4 x 2

=

                       8

Suppose the semi-annual yield is r.

Current price of bond

=

(1000 / (1 + r)^8)  + ( (60 / r) (1 - (1 + r)^(-8)))

962.13

=

(1000 / (1 + r)^8)  + ( (60 / r) (1 - (1 + r)^(-8)))

It is difficult to calculate r in the above equation.
Therefore, we will use alternative formula to determine approximate yield rate.

Yield

=

(55 + ((1000 - 962.13)/8)) / ((1000 + 962.13)/2)

=

6.09%

Annual yield rate

=

6.09%

Approximate

(e)

Face Value

=

1000

Interest rate on bond

=

10%

Semi-annual interest payment

=

1000 x 10% x (1/2)

=

50

Sale price of bond

=

1,054.36

Number of interest payments

=

10 x 2

=

                     20

Realised Yield

=

(50 + ((1,054.36 - 980)/20)) / ((1,054.36 + 980)/2)

=

5.28%

Approximate

3.(a)

When the valuation of a share is done considering the dividend growth model then it is very sensitive to the dividend growth rate as it is highly sensitive to the changes in inputs and therefore the assumption made in the model will have a direct bearing upon the share price valuation.  It needs to be noted that the valuation also makes the assumption of no linear growth pattern. The growth rate is assumed to be constant in nature and it is a common parlance that the dividend growth is not constant always (Brealey et. al, 2014). This is due to the fact that the business cycle is not constant in nature and is prone to fluctuations but this model assumes the dividend to be constant and hence it is a serious defect in this model. When the company is operating under a boom situation its earnings are high and pay more dividends but during lean times it is less and hence, there is a difference (Libby et. al, 2011).

(b)

(a)

Current dividend

=

                 1.50

Growth rate

=

0%

Cost of capital

=

15%

Current share price

=

1.5 / 15%

=

               10.00

(b)

Current dividend

=

                 0.80

Growth rate

=

5%

Cost of capital

=

15%

Current share price

=

(0.8)(1 + 5%) / (15% - 5%)

=

                 8.40

(c)

Current dividend

=

                 0.60

Growth rate in first three years

=

12%

Growth rate after 3 years

5%

Cost of capital

=

15%

Dividend at the end of 3 years

=

0.60 (1 + 12%)^3

=

             0.8430

Market price at the end of 3 years

=

(0.8430)(1 + 5%) / (15% - 5%)

=

8.8515

Current market price

=

0.60 (1 + 12%) / (1 + 15%)  +  0.60 (1 + 12%)^2 / (1 + 15%)^2  +  
0.60 (1 + 12%)^3 / (1 + 15%)^3  +  8.8515 / (1 + 15%)^3

=

                 7.53

(c)

Current price

=

33

Current dividend

=

3.6

(a)

Expected rate of return

=

3.6 / 33

=

10.91%

(b)

Required rate of return

=

10.00%

Value of preference share for investor

=

3.6 / 10%

=

36


c) Yes, an investorshould purchase Pioneer Ltd.'s preference share as the marketvalue of a share is less than the value for the investor. In other words, since the rate of return on preference shares is higher than the required rate of return, an investor should purchase preference shares (Albrecht et. al, 2011).

(d)

Dividend at the end of year 1

=

                 4.75

Dividend at the end of year 2

=

                 5.25

Dividend at the end of year 3

=

                 5.75

Dividend at the end of year 4

=

                 7.00

Growth rate after 4 years

7%

Cost of capital

=

15%

Market price at the end of 4 years

=

(7)(1 + 7%) / (15% - 7%)

=

93.625

Current market price

=

4.75 / (1 + 15%)  +  5.25 / (1 + 15%)^2  +  5.75 / (1 + 15%)^3  +  
7 / (1 + 15%)^4  +  93.625 / (1 + 15%)^4

=

               69.41

References

Albrecht, W., Stice, E. and Stice, J. (2011).  Financial accounting. Mason, OH: Thomson/South-Western.

Brealey, R, Myers, S. & Allen, F. (2014). Principles of corporate finance. New York: McGraw-Hill/Irwin.

Choi, R.D. & Meek, G.K. (2011). International accounting. Pearson.

Davies, T. & Crawford, I. (2012).  Financial accounting. Harlow, England: Pearson.

Graham, J. & Smart, S. (2012).   Introduction to corporate finance. Australia: South-Western Cengage Learning.

Horngren, C., (2013). Financial accounting. Frenchs Forest, N.S.W: Pearson Australia Group

Libby, R., Libby, P. & Short, D. (2011)   Financial accounting. New York: McGraw- Hill/Irwin.

Parrino, R., Kidwell, D. & Bates, T. (2012).  Fundamentals of corporate finance. Hoboken, NJ: Wiley

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