Equipment Replacement Optimization (Leasing Situation)

Generic Situation:

Most small businesses lease expensive equipment and must determine the least costly schedule for replacing equipment over a specified time period.

Example:

Edward North of Quick-Train Partners offers immersion classes in a number of computer programs. He uses a large number of computers for his classes and likes to keep the equipment up to date so that it will run the latest and most powerful applications. It is time to upgrade and he has two lease proposals to consider. Both contracts require Ed to pay $62,000 initially to obtain the equipment he needs, yet they differ in the amount that he would have to pay in subsequent years to replacement the equipment. Under the first contract the price to acquire new equipment would increase by 6% per year, but he would be given a trade-in credit of 60% for one year old equipment and 15% for any equipment that is two years old. Under the second contract, the price to acquire new equipment would increase by 2% per year, but he would be given a trade-in credit only of 30% for one-year-old equipment and just 10% for any equipment that is two years old.

Obviously either way he has to pay the initial $62,000, however he wants to determine which contract would allow him to minimize the remaining leasing costs over the next five years and when he should replace the equipment under the selected contract.

Profit Maximizing Solution:

The optimal solution to this problem shows that under the provisions of second contract, Ed should replace the equipment at the beginning each of the years 3 and 5 at a total (minimal) cost of $118,764.