Question

Adam has just graduated, and has a good job at a decent starting salary. He hopes to purchase his first new car. The car that Adam is considering costs $45,000. The dealer has given him three payment options:

1. Zero percent financing. Make a $7,000 down payment from his savings and finance the remainder with a 0% APR loan for 48 months. Adam has more than enough cash for the down payment, thanks to generous graduation gifts.

2. Rebate with no money down. Receive a $5,500 rebate as a discount on the car from car dealer 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 $7,000 of his saving.

3. Pay cash in full. Although Adam doesn’t have $45,000, 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.

2. 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 earns interest at a 5.4% APR (based on monthly compounding) at the bank, what would be his best purchase option for the car?

Answer 1

From the below calculations, best purchase option to buy the car is Payment Option 2

Cost of car	45000
Payment option 1				Payment option 2				Payment option 3
Down payment	7000			Down payment	0			Cash	45000
APR	0%	48 months		APR	8%	48 months		Interest foregone	10,536
Loan amount	38000			Rebate	5500
Repayment amount	38000			Loan amount	39500			Net Loss/Payment	(55,536)
Interest earned in bank	8,897			Monthly payments	964	PMT function in excel
Net payment	(36,103)			Total Repayment	46,287
				Interest earned in bank	10,536
				Net Payment	(35,751)
Bank Interest Calculation
Bank interest on cash		Option 1	Option 2
APR	5.40%	5.40%	5.40%
Total cash with Adam	45,000	38,000	45,000
Value in Year 1	47,430	40,052	47,430
Value in Year 2	49,991	42,215	49,991
Value in Year 3	52,691	44,494	52,691
Value in Year 4	55,536	46,897	55,536
Total Interest	10,536	8,897	10,536