Question

After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $43,000. The dealer has a special leasing arrangement where you pay $4,300 today and $505 per month for the next three years. If you purchase the car, you will pay it off in monthly payments over the next three years at an APR of 6 percent. You believe you will be able to sell the car for $28,000 in three years. Should you buy or lease the car? What break-even resale price in three years would make you indifferent between buying and leasing?

Answer 1

It would be better to buy the car.

Nominal 26,446.81 (break even resale price)

Step-by-step explanation:

We solve the present value of the salvage value at 6% APR

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity $28,000.0000

time 36.00

rate 0.00500

`(28000)/((1 + 0.005)^(36) ) = PV`

PV 23,398.0577

Net present worth:

23,398.06 - 43,000 = 19,601.94

Lease option

PV of the monthly payment:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 505.00

time 36

rate 0.005

`505 * (1-(1+0.005)^(-36) )/(0.005) = PV\\`

PV $16,599.8632

plus the 4,300 downpayment

present worth: -20.899,86‬

As the option from the purcahse gives a lower present worth it is preferable over the option to lease the vehicle

X - 43,000 = -20,899.86

X = 22,100.14

We have to look at which resale price the present value is equal to 22,100.14

`PV \: (1+ r)^(time) = Nominal`

Principal 22,100.14

time 36.00

rate 0.00500

`22100.14 \: (1+ 0.005)^(36) = Nominal`

Nominal 26,446.81