The packing in a cooling tower that cools condensing water for a power plant progressively deteriorates and results in gradually rising costs due to reduced plant efficiency. These costs are treated as lump sums at the end of the year, as shown in the figure. The cost is zero for the first year and then increases $1,000 per year until the packing is 16 years old, when replacement is mandatory. At a point 8 years into the life of the packing (just after the $7,000 annual cost as been assessed), a decision is to be made on the plan for the next years, i.e., whether to replace the packing or to continue with the existing packing. Money can be borrowed at 9 percent interest, compounded annually. What is the maximum amount that could be paid for the packing in order to justify its replacement?
