Question

2. (9 marks) A recent newspaper advertisement offered car buyers the opportunity to lease a new vehicle for $5,000 down plus $350 per month for 48 months. At the end of the 48 months, the car wil be returned to the dealer. Alternatively, the same car could be purchased outright for $34,000. It is estimated that in 48 months, the car could be sold for $20,000. At what interest rate (compounded monthly) are these two options equivalent?

Answer 1

Let the required monthly rate be r %

Option 1: Lease

Monthly Lease Payments = $ 350 and Upfront Downpayment = $ 5000, Lease Tenure = 48 months

Present Value of Cash Outflow = 350 x (1/r) x [1-{1/(1+r)^(48)}} + 5000

Option 2: Purchase

Upfront Immediate Price = $ 34000 and Sale Proceeds = $ 20000

Present Value of Cash Outflow = 34000 - [20000 / (1+r)^(48)]

If the two options are equivalent, then 350 x (1/r) x [1-{1/(1+r)^(48)}} + 5000 = 34000 - [20000 / (1+r)^(48)]

34000 - 5000 = 350 x (1/r) x [1-{1/(1+r)^(48)}} + [20000 / (1+r)^(48)]

29000 = 350 x (1/r) x [1-{1/(1+r)^(48)}} + [20000 / (1+r)^(48)]

Using EXCEL's Goal Seek Function/Hit and Trial Method to solve the above equation we get:

r = 0.006545 or 0.6545 %

Annual Percentage Rate = 12 x r = 12 x 0.6545 = 7.85399 % ~ 7.85 %