Question

You are trying to decide whether to keep your current car or buy a new car. If you keep your current car you will pay $350 per month (starting next month) on average for maintenance, gas, property tax and insurance. You will make these payments for 10 years. Alternatively, you can buy a new car and pay $28,000 today and $300 per month (starting next month) on average for maintenance, gas, property tax and insurance. You will make these payments for for 10 years. If your investments earn 4% APR (compounded monthly), which alternative is cheaper in present value terms and by how much?

Answer 1

Option 1: Keeping current car.

Cash flows:

Monthly expense for 10 years for maintenance, gas, insurance and tax    =	$350
Present value of the above cash flow (Discounted at the APR available on investments).= Calculated as an annuity using Excel, screen print appended below showing the values and step by step calculation	$34,569.56

Option 2: Buying new car

Cash flows:

Instant payment today =	$28,000
Monthly expense for 10 years for maintenance, gas, insurance and tax    =	$300
Present value of the above cash flow (Discounted at the APR available on investments). = Calculated as an annuity using Excel, screen print appended below showing the values and step by step calculation	$29,631.05

Total present value of cash flows =$28,000 + $29,631.05 =

$57,631.05

Conclusion:

It is seen that present value of cash outflow in option 1 (retain current car) is $34,569.56 which much less than that of option 2 which is $57,631.05. Hence retaining current car is cheaper in present value terms, by ($57,631.05-$34,569.56)= $23,061.49