Question

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

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?

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.

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