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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