Question

In: Finance

You are looking at the car that is currently selling at $65,000. Classic Autos is offering...

You are looking at the car that is currently selling at $65,000. Classic Autos is offering free credit (i.e. no interest charged on the borrowed amount) on the car. You pay $10,000 down today and then pay the remaining balance at the end of 6years. Premium Motors next door does not offer credit, but will give you $20,000 off the list price if you pay cash now. Assume annual compounding with 9% discount rate. Which of the following statement is TRUE?

A.

Premium autos is offering a better deal since its PV of cost is approximately 500 lower than that of Premium Motors.
B.

Classic autos is offering a better deal since its PV of cost is approximately 2,200 lower than that of Premium Motors.
C.

Classic autos is offering a better deal since its PV of cost is approximately 600 lower than that of Premium Motors.
D.

Premium autos is offering a better deal since its PV of cost is approximately 2,400 lower than that of Premium Motors.

Solutions

Expert Solution

Price of the car = $65,000

Classic Autos is offering free credit (i.e. no interest charged on the borrowed amount) on the car.

You pay $10,000 down today

And remaining amount = $65,000 - $10,000 = $55,000 at the end of 6 years

Annual compounding with 9% discount rate

Therefore present value of remaining amount paid at the end of 6 years

= remaining amount/ (1+discounting rate) ^number of years

= $55,000 (1+9%) ^6

= $32,794.70

Present value of total amount paid to Classic Autos = down payment + present value of remaining amount paid at the end of 6 years

= $10,000 +$32,794.70

=$42,794.70 or $42,795

Premium Motors next door does not offer credit, but will give you $20,000 off the list price if you pay cash now.

Therefore Present value of total amount paid to Premium Motors

= Price of the car – discount

= $65,000 - $20,000 = $45,000

Better deal is offered by Classic Autos as they have lower PV by $45,000 -$42,795 =$2205

Therefore true statement is

B. Classic Autos is offering a better deal since its PV of cost is approximately 2,200 lower than that of Premium Motors.

jeff jeffy answered 1 day ago
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