Optimal Equipment Lifespan Vs Maintenance Cost

One of the challenges of mine planning is to determine the most cost-effective replacement time for aging equipment. The lifespan of equipment, such as haul trucks and shovels, deployed in mining operations varies due to the nature of the material and ground conditions in which it operates. For engineering economists dealing with aging equipment, the options become an economic trade-off between higher maintenance cost versus the cost of new equipment. The discount rate plays a significant role in this decision; the higher the rate, the longer the economically optimal lifespan. Therefore, the ultimate question is: ?How can the relationship between the discount rate and the economically optimal lifespan be expressed mathematically??