The packing in a cooling tower that cools condensing water for a power planet pr

Question

The packing in a cooling tower that cools condensing water for a power planet 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. The cost is zero for the first year and then increases $1000 per year until the packing is 16 years old, when replacement is mandatory. At a point, 8 years imnto the life of the packing(just after the $7000 annual cost has been assessed), a decision is to be made on the plan for the next 8 years, i.e., whether to replace the packing or to continue with the existing packing. Money can be borrowed at 9 percent interest, compound annually. What is the maximum amount that could be paid for the packing in order to justify its replacement?

Explanation / Answer

Cost for next 8 years = $(8000+9000+10000+11000+12000+13000+14000+15000)= $ 92000

Taken rate of interest 9% compounded anually lets take amount be x.

Now, 92000=x(1+.09)^8=1.992x

so x= $ 46171.69

Hence maximum amount which can be spent to justify the replacement = $ 46171.69

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