A company needs a new car and has the following options: (1) purchase the car ca
ID: 2761453 • Letter: A
Question
A company needs a new car and has the following options: (1) purchase the car cash or (2) lease the car. They are expecting to use the car for 3 years.
If car is purchased for cash:
• Cost new, $30,000
• Salvage value, $15,000
Costs for 3 year lease:
• Amount due at signing, $3000
• 36 monthly lease payments of $400. The monthly payments are made at the beginning of the month (i.e. starting when n = 0)
The company usually invests and borrows at 12% per year compounded monthly. Determine the equivalent monthly cost of each alternative. Note: the monthly beginning of the month lease payments need to be converted to end of the month equivalent payments (i.e. payments from n = 1 36). Which option is best?
Explanation / Answer
Option 1:
Company purchase a car for Rs.30000, opportunity cost related to investment blockage @ 12.68%per annum (i.e compunded monthly interest of 12% per annum) amounts to $ 12923 for three years and car salvage value at the end of the third year is $ 15000, thereby the company total amounts incurred on opportunity and depreciated value of three years = $ 27923 (12923+15000)
Equated monthly cost is 775.64
Option 2:
Company took the same on lease basis and incurred cost for initial payment of $ 3000 and regular monthly lease payment of $ 400 at the beginning of the month for 3 years, related cost on borrowings for the respective periods.
Borrowing costs of $ 3000 for initial payment for 3 years interest rate works out to $ 4292
Total 36 monthly instalment each $ 400 (i.e from beginning of the month)
First instalment carries an interest for entire 36 months @ 12.68% (i.e cumulative interest) and subsequent month instalment reduces interest element for the balance period (1-n) (i.e 1-36) so on for next month onwards till closure of 36 months.
Total cost works out $ 17432
Total lease payment amount is $ 21723.70
Equated monthly cost is $ 603.43
As the companys borrowing and investment cost is 12% compunding monthly, the cost of lease payment at the beginning or at the end of the month does not change.
Option2 is beneficial to the company