After deciding to buy a new car, you can either lease the car or purchase it on

Question

After deciding to buy a new car, you can either lease the car or purchase it on a 5-year loan. The car you wish to buy costs $55,000. The dealer has a special leasing arrangement where you pay $2,000 today and $900 per month (at the beginning of each month) for the next 5 years. If you purchase the car, you will pay it off in monthly payments (at the end of each month) over the next 5 years at a 3.6% APR. You believe you will be able to sell the car for $18,000 in 5 years.

1. Should you buy or lease the car? Show all the equations.

2. What break-even resale price in four years would make you indifferent between buying and leasing?

Explanation / Answer

Find the PV of both options and compare:

PV of lease (Note: use the interest rate on the loan to compute the PV of the lease)

As lease payments are paid at beginning of each month, no need to calculate pv of first month payment.

N = 12*5 - 1 = 59; Rate = 6%; PMT = $900; FV = 0;

Lease cost =PV(6%/12,59,900,(0)) + $900 (first month payment) + $ 2000 initial payment)

= 45885.77 + $900 + $2000 = $48785.77

PV of loan (Price of the Car – PV of the Resale Price)

Firstly calculate pv of resale price. Then, deduct pv of resale price from cost of car to get loan amount.

N = 60 months; R = 6%; PV = 0; PMT = 0; FV = $18,000

PV = PV(6%/12,60,0,(18000)) = 13344.70

$55000 - $13344.70 = $41655.70

PV of loan is lower than PV of leasing.

Hence, purchase on a five year loan is advisable.

2.

Break-even resale price in four years:

$55000 - PV of resale price = $48785.77

PV of resale price = 6214.33

Break even resale price = 6214.33 (1+r)^n

= 6214.33*1.005^48 = $7895.24

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.