Question

2: Applications of finance (20 Mark)

Please answer the following questions. Show all your workings when calculations are required and round off your FINAL result to TWO decimal places.

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 12th 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

Following is the information provided in the question:

Option 1 : Upfront payment of $ 100,000 now.

Option 2 : Make monthly payment of $ 4500 for 24 months starting today.

Market Rate of interest: 6% p.a.

a) Calculation of present value of the two options

Option 1: PV will be $ 100,000 since the payment is made upfront at period 0.

Option 2: $ 4500*1 + $ 4500* PVAF @ 0.5%, 23m

                  = 4500+ 4500* 21.6757

                  = 4500+ 97540.65

                 = $ 102,040

Note: 24 monthly payments are made, first installment being paid at period 0. And therefore remaining 23 installment NPV is calculated using present value annuity factor ( PVAF) @ 0.5% (6% given rate is yearly and the installments are paid monthly and thus the rate has been converted to monthly) for 23 period.

Decision: Since the NPV of option 1 is less, it is a cheaper option.

b) To be indifferent to both the options, NPV of the options should be the same. Let the monthly payment be $ x, so the person is indifferent to the two options:

            $ 100,000   =    x*1 + x*21.6757

              X = 100,000

                      22.6757

                 = $ 4410

Therefore, monthly payment should be $ 4410, so the person is indifferent to the two options.

c) If the monthly payments of option 2 were to be made at the end of each month, then the present value of option 2 will be calculated by PVAF @ 0.5% for 24 periods, which will reduce the NPV of the option.

d) Calculation of effective annual interest rate (EAR) that would make you indifferent to the two options:

$ 100,000    =   $ 4500*1 + $ 4500* PVAF(%,y)

   PVAF = 95500

                   4500

              = 21.2222

Now, looking at the PVAF table, 21.2222 is the value for the rate of 8.6% p.a.

e) Following information is available:

Period 0                          $ 4500

Period 1-11                    $ 4500

Period 12-23                  $ 4000

Period 23                          ?

Now, to not be worse off by the new arrangement, NPV of the second option should be same as the original arrangement, which means the NPV should be $ 102040.65 as calculated in part (a) above.

Let the lump sum amount to be paid at the end of the contract be $ x:

          $ 102040 = $4500* 1 + $4500* PVAF (0.5%, 11m) + $4000* PVAF (0.5%, 12m) + x* PVF( 0.5%, 23m)

           102040 = 4500+ 4500* 10.6770 + 4000*10.9987 + x* 0.8916

              X = 5498.70

                      0.8916

                 = $ 6167.2275

        The lump sum amount to be paid at the end of the contract is $ 6167.