Neile looked at his mechanic and sighed. The mechanic had justpronounced a death sentence on his road-weary car. The car hadserved him well---at a cost of $500 it had lasted through fouryears of college with minimal repairs. Now, he desperately needswheels. He has just graduated, and has a good job at a decentstarting salary. He hopes to purchase his first new car. The cardealer seems very optimistic about his ability to afford the carpayments, another first for him.
The car Neile is considering is $35,000. The dealer has givenhim three payment options:
1. Zero percent financing. Make a $4000 down payment from hissavings and finance the remainder with a 0% APR loan for 48 months.Neile has more than enough cash for the down payment, thanks togenerous graduation gifs.
2. Rebate with no money down. Receive a $4000 rebate, which hewould use for the down payment (and leave his savings intact), andfinance the rest with a standard 48-month loan, with an 8% APR. Helikes 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 Neile doesn’t have $35,000, he wants to evaluate this option.His parents always paid cash when they bought a family car; Neilewonders if this really was a good idea.
Neile’s fellow graduate, Henna, was lucky. Her parents gaveher a car for graduation. Okay, it was a little Hyundai, anddefinitely not her dream car, but it was serviceable, and Hennadidn’t have to worry about buying a new car. In fact, she has beentrying to decide how much of her new salary she could save. Neileknows that with a hefty car payment, saving for retirement would bevery low on his priority list. Henna believes she could easily setaside $3000 of her $45,000 salary. She is considering putting hersavings in a stock fund. She just turned 22 and has a long way togo until retirement at age 65, and she considers this risk levelreasonable. The fund she is looking at has earned an average of 9%over the past 15 years and could be expected to continue earningthis amount, on average. While she has no current retirementsavings, five years ago Henna’s grandparents gave her a new 30-yearU.S. Treasury bond with a $10,000 face value.
Henna wants to know her retirement income if she both (1)sells her Treasury bond at its current market value and invests theproceeds in the stock fund and (2) saves an additional $3000 at theend of each year in the stock fund from now until she turns 65.Once she retires, Henna wants those savings to last for 25 yearsuntil she is 90.
Both Neile and Henna need to determine their bestoption.
Required
Q.1: What are the cash flows associated with each of Neile’sthree care financing options?
Q.2: Suppose that, similar to his parents, Neile had plenty ofcash in the bank so that he could easily afford to pay cash for thecar without running into deb now or in the foreseeable future. Ifhis cash earns interest at a 5.4% APR (based on monthlycompounding) at the bank, what would be his best purchase optionfor the car?
Q.3: Suppose Henna’s Treasury bond has a coupon interest rateof 6.5%, paid semiannually, while current Treasury bonds with thesame maturity date have a yield to maturity of 5.4435% (expressedas an APR with semiannual compounding). If she has just receivedthe bond’s 10th coupon, for how much can Henna sell her treasurybond?
Q.4: Suppose Henna sells the bond, reinvests the proceeds, andthen saves as she planned. If, indeed, Henna earns a 9% annualreturn on her savings, how much could she withdraw each year inretirement? (Assume she begins withdrawing the money from theaccount in equal amounts at the end of each year once herretirement begins.)
Q.5: Henna expects her salary to grow regularly. While thereare no guarantees, she believes an increase of 4% a year isreasonable. She plans to save $3000 the first year, and thenincrease the amount she saves by 4% each year as her salary grows.Unfortunately, prices will also grow due to inflation. SupposeHenna assumes there will be 3% inflation every year. In retirement,she will need to increase her withdrawals each year to keep up withinflation. In this case, how much can she withdraw at the end ofthe first year of her retirement? What amount does this correspondto in today’s dollars? (Hint: Build a spreadsheet in which youtrack the amount in her retirement account each year)
Q.6: Should Henna sell her Treasury bond and invest theproceeds in the stock fund? Give at least one reason for andagainst this plan.
