Crane Service Center just purchased an automobile hoist for $$40,700.$ The hoist has an $8-$year life and an estimated salvage value of $$4,100.$ Installation costs and freight charges were $$4,000$ and $$800,$ respectively. Crane uses straight$-$line depreciation.

The new hoist will be used to replace mufflers and tires on automobiles. Crane estimates that the new hoist will enable its mechanics to replace $5$ extra mufflers per week. Each muffler sells for $$78$ installed. The cost of a muffler is $$40,$ and the labor cost to install a muffler is $$13.$

$($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 $\%$

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