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

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))

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.

Explanation / Answer

A)

Let Break even Resale price be X

NPV = PV of Buying - PV of leasing

= cost minus PV of resale price - Initial pay + PV of monthly payments

= (39500 - X/1.063) - {108 + 508* [(1-1/(1+.005)36)/.005]}

= 39500 - 0.8395 X - 16806.48 = 22693.52 - 0.8395 X

At Break even sale price NPV = 0, so

NPV = 22693.52 - 0.8395X

0 = 22693.52 - 0.8395X

0.8395X = 22693.52

X = 22693.52/0.8395  = $ 27,032.19

B)

PV of buying = Purchase price - PV of resale price

= 39500 - 27500/1.063

= $ 16413.75

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