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 $31,000. The dealer has a special leasing arrangement where you pay $91 today and $491 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 $19,000 in three years.

What break-even resale price in three years would make you indifferent between buying and leasing?

Explanation / Answer

Step 1: Calculate the Present Value of the Resale Price

Present value of the resale price can be calculated with the use of present value of leasing and cost of car. The formula that can be derived is as follows:

Present Value of Resale Price = Cost of the Car - Present Value of the Lease

Present value of the lease can be calculated with the use of following formula

Present Value = Payment Made Today + P*[((1-(1+r)^-n)/r] where, P = amount of monthly payment, r =monthly interest rate and n = number of months

________________

Here, P = $491, r = 6%/12 = .50% and n = 12*3 = 36

Using this information in the above formula, we get.

Present Value of Lease = $91 + 491*[((1-(1+.50%)^-36)/.50] = $16,230.67

Present Value of Resale Price = 31,000 - 16,230.67 = $14,769.33

________

Step 2: Calculate the Break Even Resale Price

The break even resale price is the same as the future value of the present value of resale price. The formula for calculating future value is:

Future Value = PV*(1+r)^n where PV = Present Value of Resale Price, r = monthly rate of interest and n = number of months

________________

Here, PV = $14,769.33, r = 6%/12 = .50% and n = 3*12 = 36

Using these values in the above formula for future value, we get,

Break Even Resale Price = 14,769.33*(1+.50%)^36 = $17,674.17

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