Alice just finished D University and is now working for the ANZ bank as a financial analyst. Her salary is 75,000 per annum but will increase at the rate of 5% per year for the next 5 years. After 5 years, Alice can apply for a promotion to the next level where her salary would be 120,000 per year and increase at the rate of 5% per year for the next 6 years. After these 6 years, Alice is not sure whether she will be promoted again so she assumes that her salary will stay at this level for the next 20 years when she thinks about retirement.
Alice wants to buy a 2 bed room house and plans to save for a deposit for the next 5 years. Currently, the cost of the 2 bed room house in an area that Alice likes is $640,000. Based on recent market performance in the area, the price of a 2 bed room house will increase at the rate of 7% per annum.
a. Alice plans to use 50 percent of her after tax salary as savings for the deposit of the house. How much deposit would Alice is able to save after 5 years and how much does she have to borrow? Since interest rate is so low, if Alice leaves the money in the bank, she can only earn an interest of 2% per annum.
b. If the bank lends Alice at an interest rate of 6 percent per annum principle and interest, how long will Alice pay off the loan for the house? The bank requires Alice to make monthly repayment to the loan. However, she can choose to make the payment fortnightly if she wishes to. Alice continues to contribute 50 percent of her after tax salaries towards the loan.
c. Instead of putting her savings in a bank account, Alice can invest in an annuity stream which earns a rate of return of 10 percent per annum. This type of investment requires Alice to invest into an investment fund for 5 years where each year she has to put in $15,000. Recall that Alice plans save 50 percent of her after tax salary for the deposit, since she can only put $15,000 in the investment fund each year, the remaining money will be put into a bank account which earns 2% per annum. If Alice takes the investment option, how much will she able to accumulate after 5 years, how much will she have to borrow and how long before she can pay off the house?
d. To pay off the house quicker, Alice considers two other options:
Option 1: At year 5, after Alice borrows to pay for the house, instead of living in the house, she will rent the house out for $550 per week after tax and then rents a 1 bed room apartment somewhere else at the cost of $250 per week. Assume there are 4.25 weeks in a month.
Option 2: Instead of renting somewhere else to live, Alice can move back and stay with her parents and continue to rent her house out at $550 per week after tax. Each month, she only needs to contribute $600 to her parents for living expenses. With this option, Alice is able to put aside 60 percent of her after tax salary towards the payments together with the rent payment that she receives from her tenant.
How long will it take Alice to pay off the loan under each option?
e. After consider all different scenarios, please advise Alice what she should do?
Assumptions: Alice gets her salaries as a lumpsum rather than spread evenly over the course of the loan. The interest that Alice earns at the bank is calculated and paid yearly. For simplicity, you can assume there is no stamp duty and other buying costs.
Alice’s parents Peter and Mary has a $900,000 invested in a portfolio. They recently inherit shares of Luna Ltd worth $100,000. Their financial advisor provided them with the following forecast information:
Risk and Return Characteristics
Expected Monthly Returns Standard Deviation of Monthly Returns
Original Portfolio 0.67% 2.37%
Luna Ltd 1.25 2.95
The correlation coefficient of Luna stock returns with the original portfolio return is 0.4.
a. The inheritance changes Peter and Mary’s overall portfolio and they are deciding whether to keep Luna stock. Assuming that they keep the Luna stock, calculate the:
- Expected return of their new portfolio which includes Luna Ltd stock.
- Covariance of Luna stock returns with the original portfolio returns
- Standard deviation of their new portfolio, which includes the Luna stock.
b. If Peter and Mary decide to sell the Luna stock, they will invest the proceeds in risk-free government securities yielding 0.42% per month. Assuming they sell the Luna stock and replaces it with the government securities, calculate the
- Expected return of their new portfolio which includes the government securities
- Covariance of the government security returns with the original portfolio returns.
- Standard deviation of their new portfolio, which includes the government securities.
Peter and Mary also consider selling the $100,000 of Luna stock and acquire $100,000 of ABC Company common stock instead. ABC stock has exactly the same expected return and standard deviation as Luna stock. Peter comments: “It doesn’t matter whether you keep all of the Luna stock or replace it with $100,000 of ABC stock since the expected returns and standard deviations of the two stocks are exactly the same.” State whether Peter’s comment is correct or incorrect. Justify your respons