After deciding to acquire a new car, you realize you can either lease the car or
ID: 2621238 • Letter: A
Question
After deciding to acquire a new car, you realize you can either lease the car or purchase it with a two-year loan. The car you want costs $34,000. The dealer has a leasing arrangement where you pay $97 today and $497 per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of 6 percent. You believe that you will be able to sell the car for $22,000 in two years.
What is the present value of purchasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
What is the present value of leasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
What break-even resale price in two years would make you indifferent between buying and leasing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
After deciding to acquire a new car, you realize you can either lease the car or purchase it with a two-year loan. The car you want costs $34,000. The dealer has a leasing arrangement where you pay $97 today and $497 per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of 6 percent. You believe that you will be able to sell the car for $22,000 in two years.
Explanation / Answer
r = 6% per year = 0.5% per month
Leasing arrangement:
Compute PV of lease payment = PV (CF0 + CF1 + … + CF23)
PV = 97 + (497/0.005)*(1 - 1/1.005^23) = 10,869.81
Buying arrangement:
Compute present value of car considering salvage value
PV = 34000 - 22000/1.005^24 = 14,481.92
Find resale price to make indifferent
10,869.81 = 34000 - P/1.005^24
P = (34000 - 10869.81)*1.005^24 = 26,071.42
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