Question

After deciding to acquire a new car, you can either lease the car or purchase it with a four-year loan. The car you want costs $37,000. The dealer has a leasing arrangement where you pay $103 today and $503 per month for the next four years. If you purchase the car, you will pay it off in monthly payments over the next four years at an APR of 7 percent. You believe that you will be able to sell the car for $25,000 in four years. a. What is the present value of leasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the present value of purchasing the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What break-even resale price in four years would make you indifferent between buying and leasing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Part a) We need to solve the following equation to find the PV of the leasing the car:

To find the PV of the monthly PMTs We are given the following information:

PMT	503
r	7.00%
n	4
frequency	12

We need to solve the following equation to arrive at the required PV:

-nxfrequency 1- (1+ frequency PV = PMT x frequency

0.07-4x12 1- (1+ 12 0.07 PV = 503 x 12

$PV=21005.38$

Next we need to calculate the PV of Sale value of 25000

We are given the following information:

r	7.00%
n	4
frequency	12
FV	$            25,000.00

We need to solve the following equation to arrive at the required PV
$FV= PV \times (1+\frac{r}{frequency})^{frequency \times n}$

$25000= PV \times (1+\frac{0.07}{12})^{12 \times4}$

$FV=18909.97$

So the PV of the sale value = 18909.97

Part b) PV of buying the car is the purchase price of 37000

Part c) To find the BE sale price, we can reduce the purchase PV by (PV of monthly PMTs + down payment)

Then the balance is the PV of the required sale price, we can compound it for 4 years to find the actual sale price at the end of four years

Now we compound it to the end of year 4

We are given the following information

PV	15891.62
r	7.00%
n	4
frequency	12

We need to solve the following equation to arrive at the required FV
$FV= PV \times (1+\frac{r}{frequency})^{frequency \times n}$

$FV= 15891.62\times (1+\frac{0.07}{12})^{12 \times4}$

$FV=21009.58$

So the indifference sale price is $21009.58