An Australian steel company, ASM International, claims that a savings of $40\%$ of the cost of stainless steel threaded bar can be achieved by replacing machined threads with precision weld depositions. A U$.$S$.$ manufacturer of rock bolts and grout$-$in$-$fittings plans to purchase the equipment. A mechanical engineer with the company has prepared the following estimates for additional costs and savings over the next $4$ years $(16$ quarters$).$ Costs decrease for some time, then increase rapidly as the equipment ages. Savings peak at $$80,000$ for some quarters, but then decrease as expected competition takes its toll.

$\backslash$table$[[$Quarter$,$Cost, $$,$Savings, $$],[0,-350,000,-],[1,-50,000,10,000],[2,-40,000,20,000],[3,-30,000,30,000],[4,-20,000,40,000],[5,-10,000,50,000],[6-12,0,80,000],[13,-20,000,80,000],[14,-40,000,40,000],[15,-60,000,20,000],[16,-80,000,0]]$

The U$.$S$.$ manufacturer president is not sure of the time frame to plan for the use of this new technology. The decision, in part, rests upon the rate of return achievable as the years of use progress. In the past, projects must return at least $24\%$ per year to be retained.

Required:

a$.$ Determine the expected rate of return per quarter for $2$ years $(8$ quarters$)$ and beyond using a spreadsheet.

b$.$ Make a recommendation on the number of years to use the technology to economic advantage.

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