You have shopped for a new car, and the best purchase price you can get is $15,000. You have been offered a lease with 36 month-end payments of $249 and a residual value of $7,500. The interest rate that the bank would charge you to borrow money is 9 percent (APR). What is the NPV of the lease arrangement? (Ignore taxes.)

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the lease payments. Using the formula for the present value of an annuity, we get:

PV = PMT x [(1 - (1 + r)^-n)/r]
where PMT = $249, n = 36, and r = 0.0075 (which is 9%/12, since the lease payments are monthly).

PV = $249 x [(1 - (1 + 0.0075)^-36)/0.0075] = $7,366.34

Next, we need to calculate the present value of the residual value:

PV(residual) = FV/(1 + r)^n
where FV = $7,500, n = 36, and r = 0.0075

PV(residual) = $7,500/(1 + 0.0075)^36 = $5,265.28

The total present value of the lease arrangement is therefore:

PV(lease) = PV + PV(residual) = $7,366.34 + $5,265.28 = $12,631.62

Finally, we need to calculate the NPV of the lease, which is:

NPV = PV(lease) - purchase price
NPV = $12,631.62 - $15,000 = -$2,368.38

Since the NPV is negative, it means that the lease arrangement is more expensive than buying the car outright. Therefore, the best choice is to buy the car for $15,000.

You Have Shopped for a New Car, and the Best