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 four-year loan. The car you wish to buy costs $35,500. The dealer has a special leasing arrangement where you pay $100 today and $500 per month for the next four years. If you purchase the car, you will pay it off in monthly payments over the next four years at an APR of 7 percent. You believe that you will be able to sell the car for $23,500 in four years.

What is the present value of purchasing the car? (Do not round intermediate calculations and round your final 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 final answer to 2 decimal places. (e.g., 32.16))

What break-even resale price in four years would make you indifferent between buying and leasing? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

After deciding to buy a new car, you can either lease the car or purchase it with a four-year loan. The car you wish to buy costs $35,500. The dealer has a special leasing arrangement where you pay $100 today and $500 per month for the next four years. If you purchase the car, you will pay it off in monthly payments over the next four years at an APR of 7 percent. You believe that you will be able to sell the car for $23,500 in four years.

Explanation / Answer

What is the present value of purchasing the car:

Present value = Present value of car / Cumulative annuity factor (i = 7% / 12; n = 48)

= $35,500 / (1/1.07)48]

= $35,500 / 41.760

= $850

What is the present value of leasing the car:

Present value = [$500 * (1/1.07)48] + $100

= $20,980.26

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