Question

9. You are planning to buy a new car. The cost of the car is $60,000. You have been offered two payment plans: a. A 15 percent discount on the sales price of the car, followed by 60 monthly payments financed at 8 percent per year. b. No discount on the sales price of the car, followed by 60 monthly payments financed at 1.5 percent per year. If you believe your annual cost of capital is 12 percent, which payment plan is a better deal? Assume all payments occur at the end of the month.

Answer 1

Solution:

Plan A:

Cost of car = $60,000*85% = $51,000

Monthly rate of interest = 8%/12 = 0.6666666%

Monthly payment = $51,000 / Cumulative PV Factor at 0.666666% for 60 periods

= $51,000 / 49.31843 = $1,034.10

Annual cost of capital = 12%

Monthly cost of capital = 12%/12 = 1%

Present value of car = $1,034.10* cumulative PV factor at 1% for 60 periods

= $1,034.10 * 44.95504 = $46,487,83

Plant 2:

Monthly rate of interest = 1.5%/12 = 0.125%

Monthly payment = $60,000 / Cumulative PV Factor at 0.125% for 60 periods

= $51,000 / 57.77045 = $1,038.59

Annual cost of capital = 12%

Monthly cost of capital = 12%/12 = 1%

Present value of car = $1,038.59* cumulative PV factor at 1% for 60 periods

= $1,038.59 * 44.95504 = $46,690

Present value of Car under Plan A is lower than Plan B, therefore Plan A is a better deal.