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## Part A: Saving for a House Deposit

Your answers to Question 1 below should show ALL relevant workings including the formulas used and the values of the variables that will be inputted into the formulas. Final answers should be correct to two decimal places. A word version of the Formula Sheet is available on the Moodle site to assist with presentation.Christine has just completed her degree at Deakin University and is now working for the ANZ Bank.She expects her average salary to be \$91,000 per annum for the next 5 years. After 5 years, Christine can apply for a promotion to the next level where her average salary would be \$145,000 per annum for the remainder of her working life at the bank.Christine wants to buy a 2 bedroom house and plans to save for a deposit over the next 5 years. In order to borrow money from the bank Christine needs to have 20% of the purchase price of the house as a deposit.

Currently, the cost of a 2 bedroom house in an area that Christine likes is \$700,000. Based on recent market performance in the area, the price of a 2 bedroom house is expected to increase at the rate of 6% per annum.
For simplicity, assume there is no stamp duty or any other buying costs associated with the house.

Required:
(a) Christine plans to use 40% of her average salary as savings for the deposit on the house. She plans to contribute to her existing bank account at the end of every month for the next five years. Her bank account earns 2% p.a. interest compounding monthly.
(i) How much will Christine have saved after 5 years?
(ii) Does the amount saved in part (i) meet the 20% requirement from the bank as a deposit at the end of year 5?
(iii) How much does she need to borrow from the bank at the end of year 5 to buy the house?

(b) Assume the bank lends Christine the money at 5.5% p.a. interest and that she wants to pay off the loan in 30 years by making monthly instalments.
(i) Calculate the monthly instalment amount. Is Christine able to make this payment assuming she still plans to contribute no more than 40% of her average salary towards the loan? (Also assume Christine receives her promotion after 5 years).
(ii) What is the total repayment Christine must make to the bank over the 30 years and how much interest is paid?

(c) Christine is also considering paying off the loan in 15 years after which she will sell the house and upgrade to a larger property as she hopes to have a family by then.

(i) What would Christine’s monthly repayment be to the bank if she decides to pay off the loan in 15 years?
(ii) What is the total repayment Christine must make to the bank over the 15 years and how much interest is paid?
(iii) If she still plans to contribute 40% of her average salary (after her promotion) towards the loan, will she be able to make the monthly repayments?

(d) In order to pay off the house in 15 years Christine is considering the following option:
At the end of year 5, after she borrows from the bank to buy the house, she plans to rent it to tenants for \$2,200 per month and move back home to live with her parents. Her parents have asked her to contribute \$1,000 per month towards living expenses, payable at the end of each month.
(i) Will this option enable her to meet the monthly loan amount from question c part (i) above?
(ii) Based on your answers above, advise Christine if she should accept the offer from her parents.

## Part B: Investing in Australian Government Bonds

You work as an analyst in the bond research department of a wealth management firm. As a researcher, it is your job to analyse interest rates and bond prices issued by the Australian Government. Based upon your analysis, you then make recommendations to the portfolio management team on what are the best bonds to buy given their value and associated risks.A current belief amongst analysts is that global equity markets are currently overvalued.Consequently, the team is looking to take on less risk by investing in Australian government debt.A number of bonds have been selected for closer scrutiny and analysis. The table below provides an overview of each bond’s main characteristics:
Table 1: Australian 10 year Treasury bond data Face Value Maturity Coupon Coupon Frequency Yield.
Bond A \$100 5 years 2.75%p.a. Semi-annual 2.33%p.a.
Bond B \$100 7 years 3.25%pa Semi-annual 2.38%p.a.
Bond C \$100 10 years 3.25%p.a. Semi-annual 2.58%p.a.
Bond D \$100 20 years 2.75%p.a. Semi-annual 2.88%p.a.

The investment managers are unsure as to the best bonds to buy. To guide your analysis and make recommendations, you answer a series of questions.
(a) Without any calculations, state which bonds are trading at a discount, par, or at a premium to the face value. In your answer, show the relationship between coupon and yield.

(b) Calculate the current value of each bond utilising the data provided in Table 1. Show all workings.
(c) Assume that market interest rates increase across all bonds by 1%. What is the value of the bonds now? Show all workings.
(d) Now assume, for all bonds listed in Table 1, the market yields decrease by 1%. What is the value of the bonds now?

As the analyst, you expect that yields will fall by 2% per annum. Showing all workings, which bond would recommend as a purchase? Support your answer by calculating the return on the bond (Hint: (P1/P0) -1 )
(f) Define what is meant by risk free and why government debt is considered to be risk free.

You are the manager of Platinum Managed Funds. Your company offers, at the moment, a highly aggressive managed fund where 100% of wealth is allocated to stocks only. This has caused substantial concern amongst the fund’s investors due to the exposure to excess stock market volatility.

The portfolio management team has requested that you create a new portfolio that reduces risk without a major impact upon returns.As a first step, management has stated that 70% of the funds under management must be
allocated to stocks. The remainder, 30%, is to be invested in either AAA rated corporate bonds, gold or property.
In summary, the three proposed portfolios are:
? Portfolio A: 30% Gold and 70% Stocks
? Portfolio B: 30% Bonds and 70% Stocks
? Portfolio C: 30% Property and 70% Stocks

(a) By using the information in TABLE 2 (page 9) calculate the expected (average) returndenoted by E(R), and the risk (standard deviation), for each of the four assets as well as the three portfolios in Table 2.Include your answers in a copy of TABLE 2. The completed table should be submitted with your assignment. An Excel version of Table 2 is available on the Moodle site.
(b) Explain the meaning of correlation and how the correlation coefficient impacts on the risk of a portfolio. Include in your answer the meaning of the correlation coefficients of +1 and -1. What effect has the correlation coefficient had on the risk of the three portfolios above? Your answer should not exceed 500 words.
(c) Discuss the meaning of diversification in finance. What impact does diversification have on the expected return and risk for the four portfolios in Table 2? Your answer should not exceed 500 words.

Management has assumed that your investors are risk averse. Explain what is meant by risk aversion as it relates to finance. Your answer should not exceed 300 words.
(e) Of the three portfolios, which portfolio do you recommend be used by the portfolio manager. In your answer, you may utilise any calculation that is relevant. Answer should not exceed 200 words.

## Part A: Saving for a House Deposit

PART A

• The savings would be in the form of annuity with payments being made at the end.

Annuity payment = 0.4*(91000/12) = \$ 3,033.33

Total duration of annuity = 5 years or 5*12 = 60 months

Interest rate applicable = 2% p.a. or (2/12) or 0.16667% per month

The relevant formula to be applied pertains to future value of annuity.

Here, P = \$3,033.33, n = 60 and r = 0.16667%

Thus, FV = 3033.33*(1.001666760-1)/0.0016667 = \$ 191,243.6

• The relevant formula to be applied is shown below.

FV = PV (1+r)n

PV = current value of house = \$ 700,000

R= Rate of increase = 6% p.a.

N – Time period = 5 years

Hence, expected price of house after 5 years = 700000*1.065 = \$ 936,757.9

Down-payment is 20% of the cost or 0.2*936,757.9 = \$187,351.6

Since the amount computed in part (i) exceeds the above amount, hence it can be concluded that the deposit requirement would be met.

(iii) Expected price of the house at the end of 5 years = \$ 936,757.9

Deposit amount = (20/100)* 936,757.9 = \$187,351.6

Hence, required loan from the bank = \$ 936,757.9 - \$187,351.6 = \$749,406.32

PART B

1. i) Principal of bank loan (P)= \$749,406.32

Maturity of the loan (N) = 30 years or (30*12) = 360 months

Interest rate (R) = 5.5% p.a. or (5.5/12) % or 0.4583% per month

The formula for EMI computation is shown below.

EMI = P*R*(1+R)N/((1+R)N-1))

Substituting the given values, we get

EMI = (749,406.32*0.004583*1.004583360)/(1.004583360 -1) = \$4,255.04

Monthly salary of Christine after promotion = (145000/12) = \$ 12,083.33

Monthly savings = 0.4*12,083.33 = \$ 4,833.33

Clearly, the monthly savings by Christine would be sufficient to pay the monthly instalment on the bank loan.

(ii) Total repayment made by Christine during 30 years along with interest = \$4,255.04*360 = \$1,531,816.80

Amount of interest paid = Total repayment – Principal borrowed = 1,531,816.80 - 749,406.32 = \$ 782,410.47

PART C

(i) The revised duration of the loan = 15 years or 15*12 = 180 months

The formula for EMI computation is shown below.

EMI = P*R*(1+R)N/((1+R)N-1))

Substituting the new values, we get

EMI = (749,406.32*0.004583*1.004583180)/(1.004583180 -1) = \$6,123.28

(ii) Total repayment made by Christine during 15 years along with interest = \$6,123.28*180 = \$ 1,102,189.51

Amount of interest paid = Total repayment – Principal borrowed = 1,102,189.51- 749,406.32 = \$ 352,783.19

(iii) Monthly salary of Christine after promotion = (145000/12) = \$ 12,083.33

Monthly savings = 0.4*12,083.33 = \$ 4,833.33

Clearly, the monthly savings is lesser than the EMI of \$ 6,123.28 and hence Christine would not be able to pay the new EMI if she decides to save only 40%.

PART D

(i) Extra monthly cash flow from tenants = \$ 2,200

Extra living expenses payable to parents per month = \$ 1,000

Hence, incremental cash available each month = 2200-1000 = \$1,200

Monthly savings from salary = 0.4*12,083.33 = \$ 4,833.33

Total available cash = 4833.33 + 1200 = \$ 6,033.33

Clearly, the EMI amount in case of 15 year loan would still be greater and hence Christine would not be able to meet the same.

(ii) Since, she would not be able to meet the EMI for a 15 year old, hence Christine must not accept the offer.

## Part B: Investing in Australian Government Bonds

Question 2

• Bonds A, B and C would be trading at a premium to their par value. This is because the coupon rate offered by these bonds tends to exceed the respective yield. On the other hand, Bond D would be trading at a discount to the par value since the coupon rate offered by this bond is lower than the respective yield (Arnold, 2015).
• The current price of the bonds would be equal to the present value of the principal and all the coupon payments.

Bond A

Face value = \$ 100

Maturity period = 5 years

Coupon payment = 2.75% *100 = \$2.75 pa. paid semi-annually

The given yield = 2.33% p.a. or (2.33/2) or 1.165% per half year

The applicable formula is shown below.

Here, C = \$ 1.375, I = 1.165%, n= 10, M=100

Bond B

Face value = \$ 100

Maturity period = 7 years

Coupon payment = 3.25% *100 = \$3.25 pa paid semi-annually

The given yield = 2.38% p.a. or (2.38/2) or 1.19% per half year

The applicable formula is shown below.

Here, C = \$ 1.625, I = 1.19%, n= 14, M=100

Bond C

Face value = \$ 100

Maturity period = 10 years

Coupon payment = 3.25% *100 = \$3.25 pa. paid semi-annually

The given yield = 2.58% p.a. or (2.58/2) or 1.29% per half year

The applicable formula is shown below.

Here, C = \$ 1.625, I = 1.29%, n= 20, M=100

Bond D

Face value = \$ 100

Maturity period = 20 years

Coupon payment = 2.75% *100 = \$2.75pa paid semi-annually

The given yield = 2.88% p.a. or (2.88/2) or 1.44% per half year

The applicable formula is shown below.

Here, C = \$ 1.375, I = 1.44%, n= 40, M=100

•  Let the market interest rate has increased across all the four bonds by 1%.

Bond A

Here, C = \$ 1.375, I = 1.165% + 0.5% = 1.67%, n= 10, M=100

Bond B

Here, C = \$ 1.625, I = 1.19%+ 0.5%=1.69%, n= 14, M=100

Bond C

Here, C = \$ 1.625, I = 1.29%+0.5%=1.79%, n= 20, M=100

Bond D

Here, C = \$ 1.375, I = 1.44% +0.5%=1.94%, n= 40, M=100

• Let the market yields has decreased by 1%.

Bond A

Here, C = \$ 1.375, I = 1.165% - 0.5% = 0.67%, n= 10, M=100

Bond B

Here, C = \$ 1.625, I = 1.19%- 0.5%=0.69%, n= 14, M=100

Bond C

Here, C = \$ 1.625, I = 1.29%-0.5%=0.79%, n= 20, M=100.

Bond D

Here, C = \$ 1.375, I = 1.44% -0.5%=0.94%, n= 40, M=100

• Let the expected yields will fall by 2% and therefore, the interest rate would be changed.

Bond A

Here, C = \$ 1.375, I = 1.165% - 1% = 0.165%, n= 10, M=100

Therefore, price of Bond A is \$ 111.99.

Return on bond  or 9.82%

Bond B

Here, C = \$ 1.625, I = 1.19%- 1%=0.190%, n= 14, M=100

Therefore, price of Bond B is \$ 119.81.

Return on bond  or 13.47%

Bond C

Here, C = \$ 1.625, I = 1.29%-1%=0.29%, n= 20, M=100

Therefore, price of bond C is \$ 125.90.

Return on bond  or 18.91%

Bond D

Here, C = \$ 1.375, I = 1.44% -1%=0.44%, n= 40, M=100

Therefore, price of bond D is \$ 134.22

Return on bond  or 36.91%

Maximum return on bond has observed in case of bond D and hence, it can be concluded that it would be most profitable to purchase bond D.

• Risk free implies when there is no risk of default on the underlying payments. This is taken as a reference using which the applicable rates for risky clients is computed. The government debt is considered to be risk free as the risk of the government defaulting would be zero. This is because of the underlying resources available with the government coupled with the underlying credibility. Risk free government debt is essentially applicable to governments having AAA credit rating (Damodaran, 2015).

Question 3

(a) The relevant screenshot is highlighted as follows (Northington, 2015).

(b) Correlation refers to the linear relationship between two given variables. The correlation coefficient of returns of the two assets has a significant impact on the underlying portfolio risk. This is because the benefit of diversification would depend on the differences in the movements of the two stocks. For instance if the correlation coefficient between the returns of the two stocks in the portfolio is +1 or closer to this value, it implies that the two stocks would have similar movements resulting in extreme variations and thus the overall risk in the portfolio would not significantly come down on account of diversification (Berk et. al., 2013).

## Part C: Portfolio Management for a Managed Fund

On the other hand, if the correlation coefficient is -1 or close to that value, it implies that the stocks tend to move in opposite direction and thereby a natural hedge is created which tends to lead to average returns but considerably reduces the fluctuations in returns. Thus, the diversification benefits are reaped to the maximum, when the stocks forming the portfolio tend to highlight a negative correlation between their respective returns (Brealey, Myers and Allen, 2014).

The diversification benefits have been the maximum for gold and stocks portfolio since there have the highest negative correlation which has led to reduction of standard deviation.  The diversification benefits would be comparatively lesser for property and stocks portfolio since the underlying correlation is positive for these asset classes (Petty et. al., 2015).

(c ) Diversification refers to the formation of a portfolio which tends to include different type of assets or stocks. In finance, diversification is recommended for reduction of unsystematic risk related to the portfolio. This typically happens since in a well-diversified portfolio, the risk associated with a particular asset class or industry may be hedged by corresponding movements in the other asset class or industry. For instance, gold and stocks tend to have negative correlation and hence a diversified portfolio containing both these asset classes would result in lower risk both assets would act as natural hedges to each other (Parrino and Kidwell, 2014).

In case of the given portfolio, diversification has led to reduced risk which is apparent from the value of the standard deviations of the portfolios when compared with the original asset classes. Further, the returns have also reduced in comparison with the highest return asset. However, it is noteworthy that the return per unit risk has actually improved which augers well for the investors (Brealey, Myers and Allen, 2014).

(d) Risk aversion implies that the investors would tend to avoid risk and thus given two investments with same returns, they would choose the investment having lower risk. Thus, whenever there is uncertainty, the investors take step to reduce the same as the investors are averse to risk Further, it also implies that in order to invest in a risky investment, the investors would have to be given incentive in the form of higher returns. Thus, higher the perceived risk associated with an investment, higher would be the demanded returns (Damodaran, 2015). The risk averse nature of human beings tends to form the basis of modern portfolio theory which is based on the central tenet that risk and return are correlated.  In real life also, it is seen that the returns associated with debt tend to be lower than those compared with equity. The prime reason for the same is that lower risk is associated with debt in comparison with equity (Petty et. al., 2015).

(e) In order to select the best portfolio from the given three choices, it is essential to determine the return per unit risk for all the three portfolios (Arnold, 2015). This is carried out below.

Portfolio A = 11.62/20.08 = 0.58

Portfolio B = 11.10/21.04 = 0.53

Portfolio C = 13.26/26.65 = 0.50

It may be concluded that Portfolio A would be the best choice.

References

Arnold, G. (2015) Corporate Financial Management. 3rd ed. Sydney: Financial Times Management.

Berk, J., DeMarzo, P., Harford, J., Ford, G., Mollica, V., & Finch, N. (2013) Fundamentals of corporate finance, London: Pearson Higher Education

Brealey, R. A., Myers, S. C., & Allen, F. (2014) Principles of corporate finance, 2nd ed. New York: McGraw-Hill Inc.

Damodaran, A. (2015). Applied corporate finance: A user’s manual 3rd ed. New York: Wiley, John & Sons.

Northington, S. (2015) Finance, 4th ed. New York: Ferguson

Parrino, R. and Kidwell, D. (2014) Fundamentals of Corporate Finance, 3rd ed. London: Wiley Publications

Petty, J.W., Titman, S., Keown, A., Martin, J.D., Martin, P., Burrow, M., & Nguyen, H. (2015). Financial Management, Principles and Applications, 6th ed..  NSW: Pearson Education, French Forest Australia.

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