Legend service center just purchased an automobile hoist for $34,300. the hoist has an 8-year life and an estimated salvage value of $3,900. installation costs and freight charges were $3,380 and $880, respectively. legend uses straight-line depreciation. the new hoist will be used to replace mufflers and tires on automobiles. legend estimates that the new hoist will enable his mechanics to replace 5 extra mufflers per week. each muffler sells for $76 installed. the cost of a muffler is $40, and the labor cost to install a muffler is $14.(a)compute the cash payback period for the new hoist. (round answer to 2 decimal places, e. g. 10.50.)cash payback period legend service center just purchased an automobileyears(b)compute the annual rate of return for the new hoist. (round answer to 1 decimal place, e. g. 10.5.)annual rate of return legend service center just purchased an automobile%

a) 6.74 years

b) Annual rate of return = 3.6%

Explanation:

Given:

Purchasing cost of the automobile hoist = $ 34,300

Total life of the hoist = 8 years

salvage value of the hoist = $ 3,900

Installation cost of the hoist = $ 3,380

Freight charges = $ 880

Increase sales of muffler per week = 5

Selling price for muffler = $ 76

cost of a muffler = $40

labor cost to install a muffler = $14

a) cash payback period = ( initial investment) / ( Annual cash flow )

now,

Initial investment = cost of the hoist + Installation cost + Freight charges

or

Initial investment = $ 34,300 + $ 3,380 + $ 880 = $ 38,560

annual cash flow is calculated as:

= annual sales value of muffler - total material cost of muffler - labor cost of installing mufflers

= ( 5 × 52 weeks × $ 76 ) - ( 5 × 52 weeks × $ 40) - (5 × 52 weeks × $ 14)

= $ 19,760 - $ 10,400 - $ 3,640

or

Annual cash flow = $ 5,720

Hence,

Cash payback period = $ 38,560 / $ 5,720 = 6.74 years

b)  The annual rate of return is given as:

= ( Net income ) / ( initial investment  )

assuming the straight line method for depreciation,

thus,

Depreciation per year = ( Initial investment - salvage value) / Total useful life

= ( $ 38,560 - $ 3,900) / 8

or

Depreciation per year = $4,332.5

Thus,

The net income after depreciation = $ 5,720 - $ 4,332.5

or

Net income = $ 1,387.5

Hence,

Annual rate of return = $ 1,387.5 / $ 38,560

or

Annual rate of return = 3.6%

the correct choice is a