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

SOLUTION:

Calculation of Break-even sale price.

If we prefer leasing $508 per month for 36 months(3 years)

Total payment will be $508 * 36 + $108 = $18,396

By using the formula for interest compounded monthly to find the amount of total payment of $39,500 for three years with 6% interest if buying it.

P = A(1 + r / n)(nt)

P = $39,500 (1 + 0.06 / 12)(12*3)

P = $39,500 (1.1966)

P = $47,265.7

Then if you sell it for $27,500 your total cost is

$47,265.7 - $27,500 = $19,765.7

Difference between buy and lease is:

$19,765.7 - $18,396

Difference between buy and lease = $1,369.7

Calculation of Present Value of purchasing the car:

PV = $27,500 / (1 + 0.06 / 12)36           

PV = $27,500 / 1.1966

PV = $22,981.78

PV = $39,500 - $22,981.78

PV = $16,518.22

Present Value of purchasing the car = $16,518.22

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