Robert Roe has just purchased a four-year-old used car, paying $3,500 for it. A

Question

Robert Roe has just purchased a four-year-old used car, paying $3,500 for it. A friend has suggested that he determine in advance how long he should keep the car so as to ensure the greatest overall economy. Robert has decided that, because of style changes, he would not want to keep the car longer than four years, and he has estimated the annual expenses and market values for years one through four as follows. If Robert’s capital is worth 12% per year, at the end of which year should he dispose of the car?

Annual expenses:

Year 1: 950

yr 2: 1050

yr 3: 1100

Yr 4: 1550

MV at end of year

Yr1: 2250

Yr2: 1800

Yr3: 1450

Yr4: 1160

Explanation / Answer

Year 0 Year 1 Year 2 Year 3 Year 4 Purchase cost -3500 Annual Exp -950 -1050 -1100 -1550 Market value 2250 1800 1450 1160 Excess of Market Value after over annual Exp 1300 750 350 -390 Robert will dispose off the car after the end of year 3 as in year 4 annual expenses of car is in excess of market value of the car.

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