Question

Assume that you need a new car for exactly 4 years.   
You can either
1) lease the car for 4 years
2) purchase the car with a four-year loan and sell it after 4 years.

The dealer has a leasing arrangement where you pay $4,400 today and $580 per month for the next four years.

If you purchase the car, you will pay it off in monthly payments over the four years at a stated interest rate of 12 percent, paid monthly.   

In other words, your interest rate will be 1% per month.

The car you wish to buy costs $35,000. You believe that you will be able to sell the car for $15,000 in four years.

Should you buy or lease the car?   

Please show work.

Answer 1

Cost of the Car = $35,000

It can be sold for $15,000

Let us calculate the present value of resale value of the car:

Present value = Future value / (1+i)ⁿ

= $15,000 / (1+ 0.12/12)^3x12

= $15,000 / 1.43076878

= $10,483.87

Therefore, the present value of the purchase is $10,483.87

Calculation of the present value of purchase as follows:

Present value of purchase = $35,000 - $10,483.87

= 24,516.13

Now calculate the present value of leasing:

present value = Current payment + [Monthly payment x (1 – (1/1+i)ⁿ) / i]

= $4,400 + [$580 x (1 – (1/1+0.12/12)^3x12) / 0.12/12]

= $4,400 + [$580 x (1 – (1/1+0.01)³⁶) / 0.01]

= $4,400 + [$580 x (1 – (1/1.01)³⁶) / 0.01]

= $4,400 + [$580 x (1 – (0.99)³⁶) / 0.01]

= $4,400 + [$580 x (1 – 0.6989) / 0.01]

= $4,400 + [$580 x (0.301075) / 0.01]

= $4,400 + $17,462.35

= $21,862.35

By comparing the present values of the purchase and lease we can observe lease has the lower present value.

Hence lease is the best option.

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