Sunland Service Center just purchased an automobile hoist for $$36,400.$ The hoist has an $8-$year life and an estimated salvage value of $$3,200.$ Installation costs and freight charges were $$4,300$ and $$900,$ respectively. Sunland uses straight$-$line depreciation.

The new hoist will be used to replace mufflers and tires on automobiles. Sunland estimates that the new hoist will enable its mechanics to replace $5$ extra mufflers per week. Each muffler sells for $$74$ installed. The cost of a muffler is $$38,$ and the labor cost to install a muffler is $$16.$

$($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