Question

Rondo is in the market for a new car. He has narrowed his search down to 2 models. Model A costs $35,000 and Model B costs $30,000. With both cars he plans to pay cash and own them for 4 years before trading in for a new car. His research indicates that the trade in value for Model A after 4 years is 57% of the initial purchase price, while the trade in value for Model B is 43%. The interest rate is 4%. For simplicity assume that operating and maintenance costs for the models are identical. Which model is the better decision and how much "cheaper" is it than the alternative?

A,model b 1026.37

B.model a 5000.00

C.modela 1026.37

D.model b 5000.00

Answer 1

c.model a 1026.37

the following table shows the calcuation of cost of cars".

	model A	model B
initilal cost	35,000	30,000
less: present value of trade in value (see note for present value factor) (35,000*57%*0.8548) (30,000*43%*0.8548)	(17,053)	(11,027)
cost	17,947	18,973

model a is cheaper by (18973 - 17947) =>1026.(rounded off to nearest dollar)

note:

present value factor = 1 /(1+r)^n

here,

r = 4%=>0.04.

n = 4 years.

present value factor = 1 /(1.04)^4

=>0.8548