After deciding to acquire a new car, you can either lease the car or purchase it with a three-year loan. The car you want costs $38,000. The dealer has a leasing arrangement where you pay $105 today and $505 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 APR of 6 percent. You believe that you will be able to sell the car for $26,000 in three years. a. What is the present value of leasing the car

The present value of leasing the car is $16,704.86 and the break even sale price is $25483.48.

Explanation:

Solution

Given that

The monthly rate = 0.06/12 = (6%/12)

the number of period = 3 * 12 = 23

Now

The present value of leasing the car is computed below:

Payment day = $105

add: Present value of future monthly payment = 505 * (1 - (1 + (0.06/12)) ^-36 / (0.06/12)

= 166,599,86

Present value of the car = $105 + $166,599,86

=$16,704.86

Thus

The present value of purchasing the car:

Purchase cost = $38,000

Less: present value of resale = 26000 / (1 + (0.06/12)) ^-36

=21,726.77

Present value of purchasing the car is $38,000 + $21,726.77

=$16,273.23

Now

The break even sale price

Let the resale price be x

38000 - (x / ((1 + (0.06/12)) ^-36 = 16704.86

(x / ((1 + (0.06/12)) ^-36 = 38000 - 16704.86

(x / ((1 + (0.06/12)) ^-36 = 21295.14

x = ((1 + (0.06/12)) ^-36 * 212954.14

x = 25483.48

Therefore the present value of leasing the car is $16,704.86 and the break even sale price is $25483.48