One advantage of the annual worth method is that it simplifies the comparison of investment projects that are repetitive but have different cycle times. Consider the automobile purchase problem of Example 2.7. Find the annual worths of the two (single-cycle) options, and determine directly which is preferable.

Data from Example 2.7 

You are contemplating the purchase of an automobile and have narrowed the field down to two choices. Car A costs \($20,000,\) is expected to have a low maintenance cost of \($1,000\) per year (payable at the beginning of each year after the first year), but has a useful mileage life that for you translates into 4 years. Car B costs \($30,000\) and has an expected maintenance cost of \($2,000\) per year (after the first year) and a useful life of 6 years. Neither car has a salvage value. The interest rate is 10%. Which car should you buy? We analyze this choice by assuming that similar alternatives will be available in the future—we are ignoring inflation—so this purchase is one of a sequence of car purchases. To equalize the time horizon, we assume a planning period of 12 years, corresponding to three cycles of car A and two of car B.