Question

Two dealers compete to sell you a new car with a list price of $42000. Dealer A offers to sell it for $40000 if you pay cash. Dealer B offers to sell it to you for $44000 with a "0-percent financing" option: you will have to pay 48 equal monthly payments of $916.67. That is to say, Dealer B offers:

48×916.67=44000

Assume that the first monthly payment is one month after you take possession of the car.

(a) Suppose that you can finance the purchase by withdrawals from a money market fund, which earns an effective annual rate of 2% per year.

(1) If you take the financing offer from Dealer B, what is the present value of your monthly payments?

Which offer do you prefer, Dealer A’s or Dealer B’s?

(b) You always carry unpaid balances on your credit card, which charges an effective annual rate of 14% per year.

(1) If you take the financing offer from Dealer B, what is the present value of your monthly payments?

Which offer do you prefer, Dealer A’s or Dealer B’s?

Answer 1

(a) Given Information

List price of car = $42,000

Dealer A offers to sell for $40,000 if paid in cash.

Dealer B offers to sell for $44,000 with “0% financing” option in which 48 monthly installments each of $916.67 are to be paid

The purchase is being financed by withdrawal from money markets fund earning an effective annual rate of 2% pa

Now, to compare two offers, we need to find the present value of Dealer B’s offer by discounting it with 2% per annum (2%/12 or 0.167% per month)

Present Value of Dealer B’s offer (PV_B) = c/ (1+r) + c/ (1+r)² +………….+ c / (1+r)^N

=> PV_B = {c * [(1+r)^N – 1]} / [r * (1+r)^N ]

Here, c= $916.67 per month

N = 48 months

r = 0.167% per month

On putting in the values and solving

PV_B = $42,252

Now, Price quoted by Dealer A is less than PV_B.

So, Dealer A’s offer is preferable (Answer)

(b) If you are carrying unpaid balances on your credit card and paying effective annual rates of 14%, then the present value of Dealer B’s offer needs to be calculated by discounting it with 14%

Present Value of Dealer B’s offer (PV_B) = c/ (1+r) + c/ (1+r)² +………….+ c / (1+r)^N

=> PV_B = {c * [(1+r)^N – 1]} / [r * (1+r)^N ]

Here, c= $916.67 per month

N = 48 months

r = 14%/12 = 1.167% per month

On putting in the values and solving

PV_B = $ 33,545

Now, PV_B is less than quote by Dealer A. So, quote by Dealer B is preferable (Answer)