Carla Vista Service Center just purchased an automobile hoist for $$32,300.$ The hoist has an $8-$year life and an estimated salvage value

of $$3,600.$ Installation costs and freight charges were $$3,400$ and $$700,$ respectively. Carla Vista uses straight$-$line depreciation.

The new hoist will be used to replace mufflers and tires on automobiles. Carla Vista estimates that the new hoist will enable its

mechanics to replace $5$ extra mufflers per week. Each muffler sells for $$75$ installed. The cost of a muffler is $$41,$ and the labor cost to

install a muffler is $$14.$

$($a$)$

Compute the cash payback period for the new hoist.

Cash payback period

years

$($b$)$

Compute the annual rate of return for the new hoist. $($Round answer to $2$ decimal places, e$.$g$.10\mathrm{.}52\%.)$

Annual rate of return