Question

You are offered two options by the Waverley Toyota dealer for purchasing a Toyota Landcruiser 4WD.

• Option 1: Upfront where you pay $100,000 now.
• Option 2: 2- year monthly payment plan of $4500/month, starting today, with a final payment to be made 23 months from today.

a) If the market interest rate is 6% p.a., calculate the present value of each alternative and identify which alternative is cheaper. (4 marks)

b) If you could decide on the monthly payment amount for option 2, at 6% p.a. interest rate what would that amount be so that you are indifferent to the two options? (3 marks)

c) If the monthly payments of option 2 were to be made at the end of each month, how would your answer to part b) on the monthly payment amount be different? Explain briefly. NO CALCULATIONS ARE REQUIRED HERE. (3 marks)

d) What is the effective annual interest rate (EAR) that would make you indifferent to the two options? (Note that the market interest rate is not given, you need to solve for the interest rate that equates the present value of the two options). (6 marks)

e) Assume that you have chosen option 2 to purchase the car. Immediately after the 12^th monthly payment, you encounter some temporary financial difficulty and are only able to afford monthly payment of $4000. After negotiating with the dealer, they are happy for you to pay $4000 per month for the rest of the contract period and a final lump sum payment right at the end of the contract. If the market interest rate is still 6% p.a., how much would this final lump sum payment be so that you will not be worse off by this new arrangement? (4 marks)  

Answer 1

Part (a):

Present value of alternative 1 = $100,000 (Upfront payment)

Present value of option 2 = $102,040.56

Alternative 1 is cheaper.

Part (b ):

If you decide on the monthly payment amount for option 2, at 6% p.a. interest rate, amount of monthly payment so that the borrower is indifferent to the two options= $4,410.01

Part (c ):

If the monthly payments of option 2 were to be made at the end of each month, amount of payment (as per part b above) will be higher due to the interest on each payment for one month. The monthly payment will be higher by (1+r) where r= monthly interest rate.

Part (d):

Effective annual interest rate (EAR) that would make you indifferent to the two options= 8.486866%

Part (e):

If the monthly payment from 13^th payment onwards is reduced to $4,000 per month, lump sum payment needed on 24^th month is the sum of last payment ($4,000) and the balance outstanding.

Final lump sum payment= $10,698.62

Calculations as below.