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

Question

After deciding to buy a new car, you can either lease the car or purchase it with a three-year loan. The car costs $30,000. The dealer has a lease program where you pay $100 today and $400 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 a 8 percent APR. You believe that you will be able to sell the car for $20000 in three years.What is present value of leasing including the initial payment of $100? What is the cost of keeping the car for three years by purchasing i

How much is the breakeven resale price of the car in three years that would make you indifferent between leasing and buying?

How much is the breakeven resale price of the car in three years that would make you indifferent between leasing and buying?

Explanation / Answer

Soln : Leasing the car

Initial payment = $100, $400 is o be paid every month for 3 years

We need to convert the rate of 8% APR into monthly = 8/12 = 0.67%

PV of the leasing payments = 100 + 400, (P/A,0.67%,36) = 100 + 400 *(1.006736 -1)/(1.006736 *0.0067)

PV = 100 + 400*31.91 = 12864.72

In case if car is purchased, the EMI on monthly basis = 940.64

Cost of keeping the car = 940.64*36 = 33863.20, and if it is sold at the end of 3 year ,

net cost of keeping = 33863.20-20000 = 13863.20

Now, lets calculate the value of leasing cost after 3 years = 12864.72 *1.08^3 = 16206

Breakeven resale price of the car = 16206-13863.20+20000 = $22343

It will make the leasing and buying equal.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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