Jessica is in the market for a new car. She has narrowed her search down to 2 models. Model A costs $28,000 and Model B costs $18,000. With both cars she plans to pay cash and own them for 4 years before trading in for a new car. Her research indicates that the trade in value for Model A after 4 years is 52% of the initial purchase price, while the trade in value for Model B is 26%. Jessica has no emotional attachment to either model and wants to make a strictly financial decision. The interest rate is 7%. For simplicity assume that operating and maintenance costs for the models are identical every year. Which model is the better decision and how much "cheaper" is it than the alternative?
To determine which model is the better decision, we need to calculate the total cost of owning each car for 4 years.
For Model A:
Trade-in value after 4 years: $28,000 * 52% = $14,560
Net cost of Model A after 4 years: $28,000 - $14,560 = $13,440
For Model B:
Trade-in value after 4 years: $18,000 * 26% = $4,680
Net cost of Model B after 4 years: $18,000 - $4,680 = $13,320
Now we need to calculate the present value of these costs to compare them accurately.
Present value of Model A:
PV(A) = $13,440 / (1 + 7%)^4 = $10,294.31
Present value of Model B:
PV(B) = $13,320 / (1 + 7%)^4 = $10,217.27
Comparing the present values, we can see that Model B has a lower cost than Model A. The difference in cost is: $10,294.31 - $10,217.27 = $77.04
Therefore, Model B is the better financial decision and it is $77.04 "cheaper" than Model A.