Question

You currently don't have a car, but rent a car that's parked just outside your house whenever you need one. Your annual expenditure on rental cars is $2,200.

You've now considering purchasing a car that would give you the same level of convenience as your current life style. The car costs $23,000 and can be sold for $5,000 after 10 years. You'd purchase the car with money from your savings account which always earns an interest rate of 6%.
Assume that all cash flows occur at the end of each year (maybe because you drive much more around Thanksgiving and Christmas).
Part 1) What is the present value of the benefits of owning that car, ie., saving on rental expenses and selling the car?
Part 2) Should you buy the car? O No O Yes

Answer 1

To calculate the present value of car ownership benefits, we use the rental savings and future sale value, adjusted for a 6% interest rate. If the total present value is less than the cost of buying the car, it is financially advisable to purchase the car.

Step-by-step explanation:

Part 1: Present Value of Car Ownership Benefits

To calculate the present value (PV) of the benefits of owning the car, we need to consider the savings on rental expenses and the future sale of the car. We have annual rental expenses of $2,200 and a future sale value of $5,000 after 10 years. Using the given interest rate of 6%, the formula for the present value of an annuity can be used to find the present value of the rental savings, and the formula for the present value of a lump sum can be used for the sale price of the car.

The formula for the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the interest rate, and n is the number of periods. In this case, PMT = $2,200, r = 0.06, and n = 10. The present value of the car's resale value is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value.

Part 2: Should You Buy the Car?

To determine if the student should buy the car, we compare the present value of buying and owning the car to the present value of continuing to rent. If the present value of ownership is less than or equal to the present value of renting, then buying the car is a financially sound decision. Based on the calculation from Part 1, if the PV of ownership is less than $23,000, then the main answer would be yes, they should buy the car.