Question: You are considering buying a car from a local auto dealer. The dealer offers you one of two payment options:
• You can pay $30,000 cash.
• The "deferred payment plan": You can pay the dealer $5,000 cash today and a payment of $1,050 at the end of each of the next 30 months.
As an alternative to the dealer financing, you have approached a local bank, which is willing to give you a car loan of $25,000 at the rate of 1.25% per month.
a. Assuming that 1.25% is the opportunity cost, calculate the present value of all the payments on the dealer ' s deferred payment plan.
b. What is the effective interest rate being charged by the dealer? Do this calculation by preparing a spreadsheet like this (only part of the spreadsheet is shown-you have to do this calculation for all 30 months):
D E F G H
2 Month Cash payment Payment Under Difference
Deffered
payment plan
3 0 30,000 5,000 25,000 <-- =E3-F3
4 1 0 1,050 -1,050 <-- =E4-F4
5 2 0 1,050 -1,050
6 3 0 1,050 -1,050
7 4 0 1,050 -1,050
8 5 0 1,050 -1,050
9 6 0 1,050 -1,050
10 7 0 1,050 -1,050
11 8 0 1,050 -1,050
Now calculate the IRR of the difference column; this is the monthly effective interest rate on the deferred payment plan.