The monthly payment for the 72-month car loan
You ordered a Tesla Model S and will receive delivery of it this afternoon. You are deciding whether you should finance it using a loan offered by Tesla or whether you should lease it. Your personal discount rate is 4.2% APR monthly compounding.
Loan: The cash price of the car is $50,000. In addition, you will need to pay state motor vehicle tax of 6.25% on the cash price at the time of delivery. Tesla offers you a 72-month loan at a rate of 4.8% APR monthly compounding if you make a down payment of $10,000. You need to pay the initial down payment of $10,000 and the state tax on delivery. You will borrow the remaining cost using the Tesla loan offer.
Lease: Tesla offers you a 36-month lease contract with a mileage allowance of 12,000 miles per year. The initial down payment (including the first lease payment, state motor vehicle sales taxes, and other fees) is $10,000 due at delivery. The subsequent 35 lease payments are $700 per month.
a. Compute the monthly payment for the 72-month car loan.
b. Suppose you decide to buy the car and to finance it using the loan described above. You expect to trade-in your car for $25,000 after 36 months and to pay back the remaining debt on the car loan at that time. Compute the present value of the total cost of ownership over the 36 months using your discount rate of 4.2% (APR).
c. Suppose you decide instead to lease the car for 36 months. You will return your car to Tesla after 36 months and you will then need to pay a disposition fee of $395. Compute the present value of the total cost of leasing over the 36 months using your discount rate of 4.2% (APR). Is it better to purchase the car or to lease the car?
d. Part (B) uses an anticipated trade-in value of $25,000. However, this value is currently not known. At which trade-in value will the present value of buying equal the present value of leasing?
e. What other considerations besides the cash flows given above should you consider when deciding between buying and leasing a car?