Question

An $18 000 car will have a scrap value of $500 9 years from the date of purchase. 1) Using the constant-percentage depreciation method, determine the book value of the car at the end of 4 years. 2)If money can be invested at j12 = 6%, what is the monthly sinking-fund deposit necessary to replace the car if it is sold for its book value in (a) after 4 years and the price of new cars has increased at an annual rate of j1 = 5%? 3) 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%, determine whether it is more economical to buy or lease the car over a 4-year period. Assume that it can be sold for the book value found in a) if you buy the car. Only #3 plz

Answer 1

1)
Current Purchase Price = $ 18000
Scrap Value after 9 Years = $ 500
Depreciable Value = 18000-500 = $ 17500

Life of Car = 9 Years

Annual Dep = 17500/9 = $ 1944.44
Dep for 4 Years = 1944.44 * 4 = $ 7777.78

Book Value after 4 years = 18000 - 7777.78
Book Value after 4 years = $ 10,222.22

2)
Inflation Rate = 5%
Future Price after n years= Current Price * (1+Inflation Rate)ⁿ
Car Price after 4 years= 18000 * (1+5%)⁴
Car Price after 4 years= $ 21879.11

Sale Price of Old Car = Book Value = $ 10,222.22

Funds needed for new car = 21879.11 - 10222.22
Funds needed for new car = $11,656.89

Sinking fund Interest Rate,i = 6% per annum or 0.5% per month
Future Value Needed,FV = $11,656.89
Number of Months for funds, n = 4 * 12 = 48 Months

Monthly Sinking Fund (PMT) = iFV / ((1+i)ⁿ-1)
Monthly Sinking Fund (PMT) = 0.005*11656.89/ ((1+0.005)⁴⁸-1)
Monthly Sinking Fund (PMT) = 58.28/ (1.27-1)
Monthly Sinking Fund (PMT) = 58.28/ 0.27
Monthly Sinking Fund (PMT) = $ 215.48