Question

An $18 000 car will have a scrap value of $500 9 years from the date of purchase. Using the constant-percentage depreciation method, determine the book value of the car at the end of 4 years. 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%?

Answer 1

a)
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

b)
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