QuestionJuly 19, 2025

A new manufacturing machine is expected to cost 278,000 have an eight-year life. and a 30,000 salvage value. The machine will yield an annual incremental after-tax income of 35,000 after deducting the straight-line depreciation. Compute the accounting rate of return for the investment. square

A new manufacturing machine is expected to cost 278,000 have an eight-year life. and a 30,000 salvage value. The machine will yield an annual incremental after-tax income of 35,000 after deducting the straight-line depreciation. Compute the accounting rate of return for the investment. square
A new manufacturing machine is expected to cost 278,000 have an eight-year
life. and a 30,000 salvage value. The machine will yield an annual incremental
after-tax income of 35,000 after deducting the straight-line depreciation.
Compute the accounting rate of return for the investment.
square

Solution
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Answer

The accounting rate of return for the investment is approximately 23.74\%. Explanation 1. Calculate Annual Depreciation The annual depreciation is calculated using the straight-line method. The formula for straight-line depreciation is: \[ \text{Annual Depreciation} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life}} \] Substituting the given values: \[ \text{Annual Depreciation} = \frac{278,000 - 30,000}{8} = \frac{248,000}{8} = 31,000 \] 2. Determine Annual Incremental Income Before Depreciation To find the annual incremental income before depreciation, add back the annual depreciation to the after-tax income: \[ \text{Incremental Income Before Depreciation} = \text{After-Tax Income} + \text{Annual Depreciation} \] \[ = 35,000 + 31,000 = 66,000 \] 3. Compute Accounting Rate of Return (ARR) The accounting rate of return is calculated by dividing the annual incremental income before depreciation by the initial investment cost: \[ \text{ARR} = \frac{\text{Incremental Income Before Depreciation}}{\text{Initial Investment Cost}} \] \[ = \frac{66,000}{278,000} \] Calculating this gives: \[ \text{ARR} \approx 0.2374 \text{ or } 23.74\% \]

Explanation

1. Calculate Annual Depreciation<br /> The annual depreciation is calculated using the straight-line method. The formula for straight-line depreciation is:<br /><br />\[<br />\text{Annual Depreciation} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life}}<br />\]<br /><br />Substituting the given values:<br /><br />\[<br />\text{Annual Depreciation} = \frac{278,000 - 30,000}{8} = \frac{248,000}{8} = 31,000<br />\]<br /><br />2. Determine Annual Incremental Income Before Depreciation<br /> To find the annual incremental income before depreciation, add back the annual depreciation to the after-tax income:<br /><br />\[<br />\text{Incremental Income Before Depreciation} = \text{After-Tax Income} + \text{Annual Depreciation}<br />\]<br /><br />\[<br />= 35,000 + 31,000 = 66,000<br />\]<br /><br />3. Compute Accounting Rate of Return (ARR)<br /> The accounting rate of return is calculated by dividing the annual incremental income before depreciation by the initial investment cost:<br /><br />\[<br />\text{ARR} = \frac{\text{Incremental Income Before Depreciation}}{\text{Initial Investment Cost}}<br />\]<br /><br />\[<br />= \frac{66,000}{278,000}<br />\]<br /><br />Calculating this gives:<br /><br />\[<br />\text{ARR} \approx 0.2374 \text{ or } 23.74\%<br />\]
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