Final answer:
The cash payback period for the new hoist is approximately 5.85 years, calculated by dividing the total initial cost of $38,000 by the annual net cash flows from the operation of the hoist, which is $6,500.
Step-by-step explanation:
The cash payback period for the new hoist at Legend service center is calculated after factoring in the initial cost, installation charges, the salvage value, and the straight-line depreciation of the hoist. The net annual cash flow from the use of the hoist in replacing mufflers can be computed by considering the additional revenue from extra muffler replacements minus the costs associated with these replacements.
The initial cost of the hoist is the purchase price plus installation and freight charges, totaling $38,000. Over its eight-year life with a salvage value of $3,800, using straight-line depreciation, the annual depreciation expense is ($38,000 - $3,800) / 8 years = $4,275. With the service center replacing 5 extra mufflers per week, additional weekly revenue is 5 mufflers × $74 = $370. Subtracting the costs ($35 for the muffler and $14 for labor) from the sales price, the net profit per muffler is $74 - $35 - $14 = $25. Therefore, the weekly net cash flow is 5 × $25 = $125, and the annual net cash flow is $125 × 52 weeks = $6,500. The cash payback period is then the initial cost divided by the annual net cash flow, $38,000 / $6,500, resulting in approximately 5.85 years.