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 $2,400.

You've now considering purchasing a car that would give you the same level of convenience as your current life style. The car costs $28,000 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).

What is the present value of the benefits of owning that car, i.e., saving on rental expenses and selling the car?

Answer 1

HI,

Here initial cost of car = $28,000

so initial cash flow after buying car = -28000

then positive cash flow will be equal to rent saving

so Y1-Y9 cash flow = $2400

in Y10 you can sell car also

so Y10 cash flow = 2400 + 5000 = $7400

interest rate r = 6%

so

Present value of owning the car = sum of present value of cash flows

Present value of benefit of owning car = Y0 cash flow +Y1/(1+r)^1 +Y2/(1+r)^2+.......Y10/(1+r)^10

= -28000 + 2400/(1+6%)+ 2400/(1+6%)^2 +2400/(1+6%)^3 +.......2400/(1+6%)^9+7400/(1+6%)^10

= $ -7,543.82

Hence actually you will loose$-7,543.82 if you will buy the car.

Thanks