BUY OR LEASE

An $18,000 car will have a scrap value of $500 at 9 years from the date of purchase.

(a) Using the constant-percentage depreciation method, determine the book value of the car at the end of 4 years.

(b) If money can be invested at j₁₂ =6% p.a., what is the monthly sinking-fund deposit necessary to replace the car if it is sold for its book value found in (a) above after 4 years and the price of new cars has increased at an annual rate of j₁ = 5% p.a.?

(c) An identical car can be leased for 4 years at a cost of $405 paid at the beginning of each month. The contract calls for the driver to pay for fuel, repairs, licences and maintenance (but not for insurance). If the car is bought, there will be a cost of $800 at the time of purchase for 1 year of insurance, with insurance costs increasing by 4% at the beginning of each of the next 3 years. Still using j₁₂ = 6% p.a., determine whether it is more economical to buy or lease the car over a 4-year period. If the car is bought, assume that it can be sold for the book value found in (a) above.