Question

You are planning to buy a new car. The cost of the car is $50,000. You have been offered two payment plans:

• A 10 percent discount on the sales price of the car, followed by 60 monthly payments financed at 9 percent per year.

• No discount on the sales price of the car, followed by 60 monthly payments financed at 2 percent per year.

If you believe your annual cost of capital is 9 percent, which payment plan is a better deal? Assume all payments occur at the end of the month.

Can you demonstrate these in EXCEL?

Answer 1

Solution :

In first plan, present value of monthly payments discounted at 9% = Sales price of car - 10% discount on car

= $50,000 - $50,000*10% = $45,000

As monthly payment is financed at 9% only, therefore present value of monthly payments should be $45,000 only.

In 2nd plan, 60 monthly payment to be made financed at 2% without any discount on car.

Cost of car = $50,000

Monthly interest rate = 2/12 = 0.1666666%

Monthly payment amount = Cost of car / Cumulative PV Factor at 0.1666666% for 60 periods

= $50,000 / 57.05236 = $876.39

Annual cost of capital = 9%

Monthly cost of capital = 9/12 = 0.75%

Now let calculated present value of monthly payment discounted at 0.75% to compute present value of car

= $876.39 * Cumulative PV factor at 0.75% for 60 periods

= $876.39 * 48.17337

= $42,219

Nos present value of car under second option is lower than present value under first option. Therefore 2nd plan "No discount on the sales price of the car, followed by 60 monthly payments financed at 2 percent per year" is better deal.