Osman Service Center just purchased an automobile hoist for $$33,700.$ The hoist has an $8-$

year life and an estimated salvage value of $$3,640.$ Installation costs and freight charges were

$$3,550$ and $$820,$ respectively. Osman uses straight$-$line depreciation.

The new hoist will be used to replace mufflers and tires on automobiles. Osman estimates

that the new hoist will enable his mechanics to replace $6$ extra mufflers per week. Each

muffler sells for $$72$ installed. The cost of a muffler is $$39,$ and the labor cost to install a

muffler is $$13.$

a$.$ Compute the cash payback period for the new hoist.

b$.$ Compute the annual rate of return for the new hoist.