In order to continue the operation of a small chemical plant at the same capacity, it

will be necessary to make some changes on one of the reactors in the system. The

decision has been made by management that the unit must continue in service for

the next $12$ years and the company policy is that no unnecessary investments are

made unless at least an $8$ percent rate of return $($end$-$of$-$year compounding$)$ can be

obtained. Two possible ways for making a satisfactory change in the reactor are as

follows:

$(1)$ Make all the critical changes now at a cost of $$5800$ so the reactor will be

satisfactory to use for $12$ years.

$(2)$ Make some of the changes now at a cost of $$5000$ which will permit operation for

$8$ years and then make changes costing $$2500$ to permit operation for the last $4$

years.

$($a$)$ Which alternative should be selected if no inflation is anticipated over the next

$12$ years?

$($b$)$ Which alternative should be selected if inflation at a rate of $7$ percent $($end$-$of$-$year

compounding$)$ is assumed for all future costs?