Question

Crane Service Center just purchased an automobile hoist for $32100. The hoist has an 8-year life and an estimated salvage value of $3,200. Installation costs and freight charges were $3,500 and $800, respectively. Crane uses straight-line depreciation. The newhoist will be used to replace mutfiers 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 $74 installed. The cost of a muffler is $39, and the labor cost to install a muffler is $15. (a) Compute the cash payback period for the new hoist. Cashpayback period years (b) Compute the arinual rate of return for the new hoist. (Round answer to 2 decimol places, e.g. 10.528,) Annual rate of return

Answer 1

The cash payback period for the new hoist is approximately 87 weeks, and the annual rate of return is approximately 59.97%.

Step-by-step explanation:

To calculate the cash payback period for the new hoist, we need to determine how long it will take for the cash inflows from the additional muffler sales to equal the initial cash outflow for the hoist. The cash inflow from selling one muffler is $74, and the additional number of mufflers sold per week due to the hoist is 5. So, the weekly cash inflow is $370 (5 * $74). To calculate the cash payback period, we divide the initial cash outflow of $32,100 by the weekly cash inflow of $370. The cash payback period is approximately 87 weeks.

To compute the annual rate of return for the new hoist, we use the following formula: Annual Rate of Return = (Average Annual Cash Inflow / Initial Investment) * 100. The average annual cash inflows can be calculated by multiplying the weekly cash inflow of $370 by the number of weeks in a year, which is 52. So, the average annual cash inflow is $19,240 (52 * $370). Plugging in the values, we have (19,240 / 32,100) * 100 = 59.97%. Therefore, the annual rate of return for the new hoist is approximately 59.97%.

Answer 2

The cash payback period for the hoist is calculated at 7 years, whereas the annual rate of return is determined to be 24.24%. This is done by first finding the annual cash inflows, and then the annual earnings in order to compute these financial metrics.

Step-by-step explanation:

To compute the cash payback period for the new hoist, first, we must total the initial investment. The cost of the hoist is $32,100, with additional installation costs and freight charges of $3,500 and $800, respectively. This brings the total initial investment to $32,100 + $3,500 + $800 = $36,400.

To determine the annual cash inflows from the hoist, we calculate the extra revenue from mufflers each week. With 5 extra mufflers being replaced each week at a selling price of $74, where the cost is $39 and the labor cost is $15, the profit per muffler is $74 - ($39 + $15) = $20. Multiplied by 5 mufflers per week and 52 weeks per year, the annual cash inflow from mufflers would be $20× 5 × 52 = $5,200.

The cash payback period is the initial investment divided by the annual cash inflows: $36,400 / $5,200 = 7 years. Therefore, it will take 7 years for the hoist to pay back its cost.

For the annual rate of return, we look at the average annual profit generated by the hoist. Over its 8-year life, the hoist generates $5,200 annually, and with a salvage value of $3,200 at the end of 8 years, the total earnings from the hoist will be $41,600 ($5,200 × 8 + $3,200). Subtracting the initial investment, we have $41,600 - $36,400 = $5,200 as the net profit. Dividing this by the life of the investment, we get an average profit of $5,200 / 8 = $650 per year.

The investment cost minus the salvage value is the depreciable amount: $36,400 - $3,200 = $33,200. With straight-line depreciation, the annual depreciation is $33,200 / 8 = $4,150. Adding the depreciation back to the net profit, the annual earnings are $650 + $4,150 = $4,800. The annual rate of return is thus the annual earnings divided by the average investment: $4,800 / (($36,400 + $3,200) / 2) = $4,800 / $19,800 = 0.2424, or 24.24% when rounded to two decimal places.