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

ID: 2647477 • Letter: A

Question

After deciding to buy a new car, you can either lease the car or purchase it on a three-year loan. The car you wish to buy costs $39,500. The dealer has a special leasing arrangement where you pay $108 today and $508 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 6 percent APR. You believe you will be able to sell the car for $27,500 in three years.

What break-even resale price in three 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))

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))

Explanation / Answer

Lets assume the Break even sales price be X Hence the present value shall be equal of both Purchase and lease option Buy option Present value Present Value of instalments 39500 Terminal value -0.8396 * X PV of Purchase option 39500 - 0.8396*X Lease option Present value Amount PVF (6%) PV Initial payment 108 1.00000 $ 108.00 Monthly payments 508 32.87102 $ 16,698.48 PV of lease option $ 16,806.48 So, 39500-0.8396*X = 16806.48 X = $27028.97 Hence the breakeven Sale price = $27028.97 Lease option Present value Amount PVF (6%) PV Present Value of instalments 39500 1.00000 $ 39,500.00 Terminal value -27500 0.8396 $ (23,089.00) PV of lease option $ 16,411.00

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

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

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