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

Answer:

Part 1) Present value of the benefits of owning that car: -$4,016

Part 2) As owning the car would give the same level of convenience and its present value of benefits is negative, the car should not be bought.

Explanation:

Part 1 explanation and calculation are shown as below:

The present value of the benefits of owning a car arises and is determined from and by the present value following cash flows, which are discounted at the saving rate 6% through out 10 years:

PV of Saving on annual rental cars expenditure + PV of the proceed of car's disposal after 10 years - Car's purchasing price.

in which: PV of Saving on annual rental cars expenditure = ( 2,200/6%) / [ 1 - (1+6%)^(-10)] = $16,192;

                  PV of the proceed of car's disposal after 10 years = 5,000/ (1+6%)^10 = $2,792;

                    Car's purchasing price = $23,000

Thus, present value of the benefits of owning a car = 16,192 + 2,792 - 23,000 = - $4,016