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%