1. Ethan Tran's life is changing rapidly. He has just started his first job after graduating from Central with a business degree. But there are big changes on the horizon (well, big changes that come in small packages): His significant other is pregnant and the baby is due around the first week of July 2016.
Of course his little pride-and-joy is going to be cute AND smart. After much consultation, his significant other and he have decided that they want to send the little one to a private college (when the time comes). Private colleges are very expensive. The average current cost is estimated to be around $36,993 for one year. This cost covers tuition, fees, room, and board and is based on a private, four-year school in the United States. Ethan expects these costs to increase by 3.9% per year over the foreseeable future (approximately the same rate as inflation.)
Their child will most likely begin school eighteen (18) years after birth. Schools tend to demand payments upfront. Assume the cost of the whole first year tuition is due in July 2034. The whole second year tuition is due in July 2035, etc. Ethan and his wife expects to invest their money in a manner that returns 7.50% per year over the foreseeable future. They want to start saving soon. In fact, they plan to invest money every year. To be precise, they will put away money once a year, every July, starting when the baby is born, and ending in July, 2033.
A. Suppose they want to save the same amount each year in nominal dollars. How much will they have to save each year so that there is enough money to send their child to college?
B. In the first part of this problem, you helped them calculate the nominal amount saved each year. Of course, in real terms, the value of these amounts gets less and less over time due to inflation. Suppose they want to save the same real amount each year. How much will they have to save each year so that there is enough money to send their child to college? In addition, provide the actual (increasing) payments in nominal dollars made each year.
2. It is April 1 and your mother tells you that the forward rate for year 2, i.e. f1,2, is -5% (yes...negative!). You ask her about the current 1-year spot rate, which she informs you is 5%. Not having been born yesterday, you ask her to wait while you make a few calculations. Note that all yields are effective annual yields.
A. If what you mother says is true, what would you have to pay back in two years if you borrowed $100 today?
B. If you invested $100 in a 1-year bond today, what would be the value of your investment one year from now?
C. Imagine yourself one year from today with the amount obtained from the 1-year bond investment from part B. There is always a virtually risk-free way to invest your money for the second year. What is this alternative and what is its rate of return?
D. Using your answers from parts A, B and C, describe an arbitrage strategy that allows you to borrow $100 at a very low rate for two years and invest the amount borrowed at a higher rate. What is your arbitrage profit?
E. Is your mother pulling your leg? Justify your answer
3. You want to purchase a brand new 2016BigUmer. Your nearest dealership, Big Motors, is selling it for $25,000. You have enough cash in the bank, currently earning 15% interest (APR with monthly compounding). Big Motors is also promoting the following two financing schemes:
- A lease with $2,000 down, $450 per month for 36 months starting next month, and a residual value of $18,000 in 3 years. Note that this means that you have the choice of buying the car in three years for $18,000 or simply giving it back to the dealership.
- A 3-year, $5,000 down, 0% loan. Note that this means the car is yours after 36 monthly payments.
After some research, you also find that 3-year-old used BigUmers sell for one third of their original purchase price in an active used car market (i.e. you have no trouble either buying or selling the car at that discounted price either today or in three years).
What is the optimal purchasing strategy?
A. Take the lease and buy the car at the end of the 3-year period
B. Take the lease, return the car at the end of the 3-year period and buy a used car
C. Take the loan
D. Buy the car with cash.