| FIN304: Decision Making for Financial Managers |
Question 1
You have just graduated, are dead broke, but would still like to buy a new car so that you can show it off on Instagram. Your rich Aunt Amy, who is a retired investment banker at the age of 35 because she knew better, is willing to lend you the money to buy the car, as long as you promise to pay her back in four years.
You propose to pay her the rate of interest she would otherwise get by putting the money in the bank, which has deposit and loan rates of 2% and 6%, respectively. Based on your projected income and living expenses, you anticipate that you will be able to pay her $30,000, $40,000, $45,000, and $50,000 at the end of each of the next four years, respectively.
(a) If your aunt accepted your proposal, how much would she be willing to lend you today?
(b) How much would your aunt have in four (4) years if she chooses not to lend you the money?
(c) How much would your aunt have in four (4) years if she chooses to lend you the money?
(d) Based on your calculations in parts (b) and (c), you believe your aunt should be indifferent between lending you the money or putting the money in the bank. Discuss whether she would agree with your assessment.
(e) Suppose your aunt proposes to make you indifferent between borrowing from her or borrowing from the bank instead. How much would she be willing to lend you today?
(f) You and your aunt eventually agree to an interest rate of 4%. Explain whether you win, whether your aunt wins, and how such an outcome can be possible.
Question 2
You would like to purchase a private condominium that costs $1.2 million, and you are shopping around for a housing loan. As this is your first housing loan, the Monetary Authority of Singapore (MAS) allows you to have a loan-to-value (LTV) limit of 75%. Also, you are required to maintain a total debt servicing ratio (TDSR) of 60%. The best deal you could find is by the Digital Bank of Singapore (DBS), which offers a fixed-rate loan of 1.8% per annum and makes a net interest margin of 0.6% per annum. You would like to take out a loan for 35 years and do not have any other outstanding debt.
(a) How much must your gross monthly income at least be in order to afford this condominium?
(b) Suppose you are able to take out this loan. Without constructing a loan amortization schedule, calculate the total amount of interest you would pay over the life of the loan.
(c) Is your calculation in part (b) technically appropriate? If yes, explain why. If not, come up with an alternative measure of the dollar cost of borrowing that is technically appropriate and interpret that measure
While you are browsing the bank’s website, you find that DBS quotes an interest rate of 1.6% per annum on a car loan. Incidentally, you are thinking about buying that cheapest possible Mercedes A-Class Saloon, which costs $180,000. MAS rules restrict financing to 60% of this car for a maximum loan tenure of 7 years which you plan to max out. The terms of the loan contract state that monthly payments are computed using the following formula:
(d) Assess whether the housing loan or the car loan is more expensive by comparing appropriate annual rates.
(e) If the conclusion reached in part (d) is different from the conclusion reached through a comparison of rates quoted by DBS, explain why. Also, explain why the rate of one loan type should be higher than the rate of another loan type.
Question 3
Your friend’s father just turned 55 and is thinking of joining CPF LIFE. He tells you that if he sets aside the Basic Retirement Sum (BRS) of $90,500 today, he can expect an approximate monthly payout from age 65 of $780 for as long as he shall live. Alternatively, if he sets aside the Full Retirement Sum (FRS) of $181,000 today, he can expect an approximate monthly payout from age 65 of $1,440. Assume that the interest rate is 4% and that compounding occurs monthly.
(a) What is the breakeven age for the BRS plan?
(b) What is the breakeven age for the FRS plan?
(c) At what life expectancy would your friend’s father be indifferent between the two (2) plans? Which plan should he choose given male life expectancy in Singapore?
