FUNDAMENTALS OF FINANCE ASSIGNMENT -
QUESTION 1 (FINANCIAL MATHEMATICS) -
Meryl Crepe is a French student who is looking to study abroad in Australia at Deakin University. She intends to begin her studies on the 31 January 2019. She intends to undertake a Ph.D. in computer science which is a 4-year course. The Australian university informs her that the fee for a Ph.D. is $12,000 per annum. The first fee is due on the 31 January 2019 and falls due every following year on the same date.
Unfortunately, Meryl has not been able to gain sponsorship or a scholarship either from France or Australia for the Ph.D. She is fearful that she will no longer be able to make her dream come true of studying abroad.
Desperate to undertake the Ph.D., Meryl turns to her family for help. A kind uncle of hers, Pierre, offers to fund her for the full Ph.D. enrolment period. He offers to pay the $12,000 every year for the 4 years. Pierre is extremely wealthy, and there are no constraints on how much he is willing to pay.
He states he will deposit an equal sum of money into a savings account every month. The first deposit will be made on the 1 February 2018. Pierre intends to make 12 regular deposits at the beginning of each month. The last deposit will be made on the 1 January 2019. Interest rates have remained relatively constant in recent history and are believed to remain steady at 4% p.a.
Answer the following questions in relation to the case study. Your answer must also be expressed in a sentence. Show full workings.
a) To find the best solution to Meryl's financial problem, Pierre decides that he will make a deposit at the beginning of every month. Discuss what is the advantage of investing immediately over delaying to the end of the month?
b) What is the total present value of the four university payments as at 31 January 2019? What is the equivalent present value as at 31 January 2018?
c) How much money will Pierre need to deposit at the beginning of every month to ensure there are sufficient funds to cover all four payments?
d) Pierre has made his first withdrawal of $12,000 on the 1 February 2019 to pay the first of the four fees. How much is left in the account after the first withdrawal?
e) Throughout 2019, inflation and university costs have been steadily rising. Immediately after the first year, Meryl is shocked to find out that her fees are set to rise consecutively for her final three years of study. The university informs her now that, the future fee schedule will be:
- 1 February 2020: 14,000
- 1 February 2021: 16,000
- 1 February 2022: 19,000
Meryl immediately informs her uncle of the new outcome! (For your calculations, take the 1 February 2020 as the present value date). Pierre recalculates the total present value of the new unequal cash outflow. How much, in present value terms, will Pierre pay for the remaining three years? Assume the discount rate now is 6% p.a.
f) Graphically illustrate your answer from part e) by utilising a time line. In your time line show the cash flows in part e), their associated present values, and the present value of total cash flow stream.
Part B -
Many years have passed and Dr Meryl has found success in the commercial world working as an investment banker rather than as a computer scientist.
Her beloved uncle had passed away recently. To show her gratitude and to honour her uncle, she has decided to establish a scholarship fund which will pay an annual scholarship to a lucky international student to undertake a Ph.D. in Australia.
To this end, she decides she will pay out of this fund $15,000 every year indefinitely. Having a strong maths background and given now she is an investment banker, Meryl realises that a perpetuity is perhaps the best way to finance the gift.
g) What is a perpetuity in finance and why is it used?
h) Meryl decides to adopt a perpetuity model to determine how much she should initially deposit in the scholarship fund. Calculate the present value of a perpetuity payments of $15,000 per year if the discount rate is 18%.
i) Meryl believes it may be too difficult to achieve a return of 8% p.a. indefinitely and searches for an alternative investment to achieve her desire for the creation on a scholarship fund. In her search, she finds something extraordinary. In 1648, the Dutch government issued a bond that would exist forever. It is currently owned by Yale University and pays interest of 2.5% interest!
Meryl thinks such an investment might be the easiest. Searching she finds two potential perpetual bonds from China. One is from Nanyang Commercial Bank, with an interest rate of 5% and the other from Dianjian Haiyu (an infrastructure company) paying 3.5%.
What are the present values of these two bonds? (Hint: use the perpetuity formula again here). How much more expensive are either compared to the answer in part h)?
QUESTION 2 (EQUITIES) -
Assume it is 2016. Two ASX listed companies, Virgin Australia and NextDC, are looking to issue new shares to existing shareholders sometime during the year.
On moodle, you can find the Rights Entitlement booklets for both companies.
The provision of new shares is termed a rights issue or offer.
It is assumed that currently you have equity investments in both companies. In Virgin, it is assumed you have invested $9,997.50 and own 46,500 shares. In NextDC, you own 2,267 shares for a total investment of approximately $9,997.47.
a) What is a rights issue? Why would a company undertake a rights issue?
b) Both companies are in substantially different industries. Identify these two industries and briefly describe the business activities of the two companies.
c) As a shareholder in both companies, you have a keen and active interest in how the funds will be used by these companies. Discuss how both Virgin Australia and NextDC are looking to use the new capital raising? To answer this question, you may either refer to the rights entitlement booklets on moodle or find other, referenced secondary sources. If you had a choice, which utilisation of capital seems the most beneficial to investors?
d) List the main features of both rights issue offers. In your answer consider:
- The retail investment offer price;
- The ratio of the rights issue;
- The total offer size in terms of number of shares; and
- The gross proceeds that will be raised by the company
e) What is the process to purchase the extra shares being made available? (Hint: go to the booklets on Moodle)
f) Assume your current holdings as at the end of the offer for each company is as follows:
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Table 1: Current Investment
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Company
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Date
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Current Market Share price
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Number of shares owned
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Total Investment in company
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Virgin
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27 July 2016
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0.215
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46,500 shares
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$9,997.50
|
|
NextDC
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26 September (2017)
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$4.41
|
2,267 shares
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$9,997.47
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If you invest in both companies:
i. By how much will your shareholdings increase by?
ii. How much will you have to pay in total to each company for the rights issue shares?
iii. What is your total investment in each company after taking up the rights issue?
For both questions assume you have fully taken up the rights offer. Use Table 2 (attached) for your answer.
g) You have held onto your investments in the two companies until now. Check the adjusted closing share price of both companies as at 1 March 2018.
Did you observe a major increase in either of the two investments since the rights issue?
QUESTION 3 (PORTFOLIOS AND RISK AND RETURN) -
You have recently been appointed chief investment officer of a major US university's endowment fund. The endowment has recently received a substantial charitable donation of $100million. The current board of trustees is uncertain as to the best way to invest and create a portfolio. The board of trustees is a group of prominent individuals whose knowledge of modern portfolio theory and practice is poor and lacking. They have requested you provide a number of responses to a series of questions and problems.
a) Using appropriate academic references, explain the concepts of risk, standard deviation, systematic risk, beta, unsystematic risk in the context of finance theory.
b) Using appropriate academic references, discuss the meaning of diversification in finance.
c) So far, the board has invested in only two companies, Apple and Alphabet Inc. (Google). Discuss the potential problems associated with this portfolio. (Hint: The discussion should emphasise how diversification is achieved and the type of companies they have invested in).
d) After your presentation, the board of trustees believe the current portfolio strategy is far too concentrated in one industry and country: technology and the Unite States.
The current portfolio is comprised of:
50% Alphabet Inc. stock (formerly Google)
50% Apple, Inc. stock
They approach you again and request that you create a number of new portfolios. The specifically request that you run an analysis on the following portfolio combinations.
Portfolio 1: Apple 50%; Rio Tinto 50%
Portfolio 2: Apple 50%; Alibaba 50%
Portfolio 3: Alphabet 50%; Rio Tinto 50%
Portfolio 4: Alphabet 50%; Alibaba 50%
By using the information in TABLE 3 (page 7) calculate the expected (average) return, denoted by E(R), and the risk (standard deviation), for each of the stocks as well as the five portfolios (including the current portfolio) above. Include your answers in the table. The completed table should be submitted with your assignment. An Excel version of Table 3 spreadsheet is available on the Moodle site.
e) Discuss the impact that diversification has had on the expected return and risk for each of the portfolios. In your answer consider not just the statistics but also consider the industries.
f) Assume the board of directors are risk averse, which portfolio do you recommend they invest in. In your answer, you must define what is meant by risk aversion. You may include any other calculations that you think might help you.
Attachment:- Assignment File.rar