[hallemxlll]

Adam Rust looked at his mechanic and sighed. The mechanic had just pronounced a death sentence on his road-weary car. The car had served him well—at a cost of $500 it had lasted through four years of college with minimal repairs. Now, he desperately needs wheels. He has just graduated, and has a good job at a decent starting salary. He hopes to purchase his first new car. The car dealer seems very optimistic about his ability to afford the car payments, another first for him.
The car Adam is considering costs $35,000. The dealer has offered him three payment options:
1. Zero percent financing. Make a $4000 down payment from his savings and finance the remainder with a 0% APR loan for 48 months, requiring equal monthly payments over the 48 month term of the loan. Adam has more than enough cash for the down payment, thanks to generous graduation gifts.
2. Rebate with no money down. Receive a $4000 rebate, which he would use for the down payment (and leave his savings intact), and finance the rest with a standard 48-month loan, with an 8% APR. He likes this option, as he could think of many other uses for the $4000.
3. Pay Cash. Get the $4000 rebate and pay the rest with cash. While Adam doesn’t have $35,000, he still wants to evaluate this option. His parents always paid cash when they bought a family car: Adam wonders if this really was a good idea.
Adam’s fellow graduate, Jenna Hawthorne, was lucky. Her parents gave her a car for graduation. Okay, it was a little Hyundai, and definitely not her dream car, but it was serviceable, and Jenna didn’t have to worry about buying a new car. In fact, Jenna has been trying to decide how much of her new salary she could save. Jenna believes she could easily set aside $3000 per year of her $45,000 annual salary. She is considering putting her savings in a stock fund. She just turned 22 years old and has a long way to go until retirement at age 65, and she considers the risk level of the stock fund reasonable for such a long term plan. The stock fund she is considering has earned an average annual rate of 9% over the past 15 years and could be expected to continue earning this annual rate, on average, for the foreseeable future. While she has no current retirement savings, five years ago Jenna’s grandparents gave her a new 30-year U.S. Treasury bond with a $10,000 face value.
Jenna wants to know her retirement income if she (1) sells her Treasury bond at its current market value and invests the proceeds in the stock fund, and (2) saves an additional $3000 at the end of each year in the stock fund from now until she turns 65. Once she retires, Jenna wants those savings to last at least for 25 years, until she is 90.
Both Adam and Jenna need to determine their best options.


1. (9 points) What are the cash flows associated with each of Adam’s three car purchase options? Prepare a timeline for each.























2. (5 points) Suppose that, similar to his parents, Adam had plenty of cash in the bank so that he could easily afford to pay cash for the car without running into debt now or in the foreseeable future. If his cash earned interest at a 5.4% APR (based on monthly compounding) at the bank, what would be his best purchase option for the car?









3. (5 points) In fact, Adam doesn’t have sufficient cash to cover all his debts including his (substantial) student loans. His student loans have a 10% APR for monthly payments, and any money spent on the car could not be used to pay down the student loans. What is the best option for Adam now? (Hint: Note that having an extra $1 today saves Adam roughly $1.10 next year because he can pay down the student loans. So, 10% APR for monthly payments is Adam’s opportunity cost for this question.)









4. (5 points) Suppose, instead, that Adam has more than $4,000 of credit card debt, with an 18% APR for monthly payments, and he doubts he will pay off this debt completely before he pays off the car. What is Adam’s best option now?










5. (5 points) Suppose Jenna’s Treasury bond has a coupon interest rate of 6.5%, paid semiannually and current Treasury bonds with the same maturity date have a yield to maturity of 5.4435% (expressed as an APR with semiannual compounding). If she has just received the bond’s tenth coupon, for how much can Jenna sell her treasury bond now?








6. (10 points) Suppose Jenna sells the bond, invests the proceeds in the stock fund, and then saves an additional $3000 at the end of each year as she planned. If, indeed, Jenna continues to earn a 9% effective annual return on her stock fund, how much could she withdraw each year in retirement? (Assume she begins withdrawing the money from the account in equal amounts at the end of each year once her retirement begins.)













7. (4 points) Suppose Jenna assumes there will be 3% inflation every year until she turns 90. What would be the value in today’s dollars (today’s purchasing power) of her fist year retirement income? For her last year retirement income?





8. (5 points) At the last minute, Jenna considers investing the proceeds from the sale of her treasury bond into Coca-Cola stock. The stock is currently selling at a price of $55.55 per share. The stock just paid an annual dividend of $1.76 and she expects the dividend to grow at 4% annually. If the next dividend is due in one year, what expected return is Coca-Cola stock offering?










9. (2 points) Should Jenna invest her money in the stock