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 three-year loan. The car you wish to buy costs $35,000. The dealer has a special leasing arrangement where you pay $1 today and $450 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 an 8 percent APR. You believe that you will be able to sell the car for $23,000 in three years. Should you buy or lease the car? What breakeven resale price in three years would make you indifferent between buying and leasing?

Explanation / Answer

Observe that to select one among the 2 options the present value needs to be calculated and the option with the lesser present value will be chosen.

Option 1 lease

Use the following values to calculate the present value of the leasing agreement.

PMT that is amount paid every month is $450.

The interest is 8% annual; therefore convert it into monthly rate as follows:

8/12=0.6666% monthly.

$1 is paid today.

Time is 3 years, therefore 36 months.

Observe that the future value is 0.

Calculate the present value using the PV function in spreadsheet

PV=$14,360.31

Since $1 was paid at the beginning, therefore total present value is $14360.31+$1

=14361.31.

Option 2 purchase

Use the following values to calculate the present value of the purchase agreement.

Selling price of the car is $23000, therefore the future value of the option is 23000.

Observe that time and interest is same.

Calculate the present value as follows:

Present value=$18106.86.

The purchase price is 35000.

Therefore 35000-18106.86

=$16893.14.

Observe that the present value of the leasing agreement is less therefore leasing option will be chosen.

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