Zack just got a job in the Boston office of Charles Consulting after he graduated from Northeastern. Moving out of the dorm, Zack decided to buy a new car for his commuting need. He did some research and found two cars he likes. And he is indifferent between the two cars. One is an American car. (Lets call this car A car) The other is a Japanese car. (Lets call this car J car) So the only factor that can help him to make the final decision is the present value of the cash outflows for the two cars.

The sticker prices of Japanese cars are usually close to their dealers bottom line price. Therefore, buyers do not have much room to bargain. In contrast, the sticker prices of American cars are usually significantly higher than the bottom line price, which leaves some room for bargaining. In order to find the best deal, Zack went around to talk with dealers. With some effort and bargaining, a dealer agreed to sell him an A car with a sticker price of $37,000 for $29,000. Another dealer agrees to sell him a J car with a sticker price of $31,000 for $28,500.

Zack also found that he has two options to pay for the new car. One is to pay with cash from his saving account. The other is to take a 5-year auto loan. Besides buying the car, Zack can also lease the car for three years. If Zack leases the car, the residual value of the car after three years is 50% of the sticker price. This means that the present value of the lease payments and the residual value should equal the final price. Currently, there are promotions going on for the leasing option and the financing option. For the auto loan option, the current promotion interest rate is 0% APR. For the leasing option, the monthly payment for car A is $270 plus sales tax and excise tax. The monthly payment for car J is $290. The detailed terms for the auto loan and the leasing option are listed in the following table.

Cars	A	J
Sticker Price (MSRP)	$37,000	$31,000
Final Price	$29,000	$28,500
Sales Tax	6.25%	6.25%
Trade-in Value after 3 years	$16,000	$18,000
Trade-in Value after 6 years	$9,300	$11,000

The sales tax is based on the payment. The buyer needs to pay the sales tax based on the final price if he chooses to buy the car. If the buyer is leasing the car, he just needs to pay the sales tax base on the lease payment. However, since lease payment is paid every month, the sales tax is also due every month based on the lease payment. The excise tax is due on an annual basis to the government. The tax rate for the first 4 years are 2.25%, 1.5%, 1%, and 0.625% respectively. Starting in the fifth year, the excise tax rate becomes 0.25% forever. The base of the excise tax rate is the sticker price. If Zack chooses to lease the car, instead of paying one excise tax payment according to the excise tax rate every year, he needs to pay a $51 excise tax every month with the lease payment. If Zack chooses to buy a car, he is planning to sell the car after six years because he worries about the maintenance cost after six years.

With three different options and a lot of details, it is really hard for a typical consumer to make a decision. Comparing the three options are like comparing apples to oranges. Fortunately, Zack has a smart friend (you) who is an expert in finance. Now Zack is asking for your help to decide which option is the best for him. Please help Zack to figure out the best option.

Hint:

Present Value

The average historical return on S&P 500 index is about 6%.

If you need more information, Google is a good helper.

With the buying option, Zack is going to keep it for six years. Therefore, for the leasing option, you should consider leasing a car for three years, then leasing another new car with the same price (including new excise tax) for three years. Remember to discount the cash flows in the second 3-year period.

You can make reasonable assumptions.

Can I please get a quantitative analysis and a brief explanation as to which method is better? Leasing or Loan?