To determine the expected after-tax cash flow from selling the equipment in three years, we need to calculate the accumulated depreciation over those three years, compute the book value at the time of sale, determine any gain or loss on the sale, and then calculate the tax effect and cash flow.

Step-by-Step Solution

1. Initial Purchase Price and Depreciation

   • Purchase price: $P = 268,000$
   • Depreciation rates (accelerated) over the years:
     • Year 1: 44%
     • Year 2: 23%
     • Year 3: 16%

2. Calculate Depreciation for Each Year $\text{Depreciation Year 1} = 268,000 \times 0.44 = 117,920$ $\text{Depreciation Year 2} = 268,000 \times 0.23 = 61,640$ $\text{Depreciation Year 3} = 268,000 \times 0.16 = 42,880$

3. Accumulated Depreciation After 3 Years $\text{Total Depreciation} = 117,920 + 61,640 + 42,880 = 222,440$

4. Calculate Book Value at the End of Year 3 $\text{Book Value} = \text{Initial Cost} - \text{Accumulated Depreciation}$ $= 268,000 - 222,440 = 45,560$

5. Determine Gain or Loss on Sale

   • Selling Price at end of Year 3: $49,000$
   • Book Value at end of Year 3: $45,560$

   Gain on Sale: $\text{Gain} = 49,000 - 45,560 = 3,440$

6. Calculate Tax on Gain

   • Tax rate: 20% $\text{Tax on Gain} = 3,440 \times 0.20 = 688$

7. After-Tax Cash Flow from Sale $\text{After-Tax Cash Flow} = \text{Selling Price} - \text{Tax on Gain}$ $= 49,000 - 688 = 48,312$

Final Answer

The expected after-tax cash flow from selling the equipment is $48,312.

Would you like further details or have any questions?

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Here are some questions that expand on this topic:

1. How would changes in the depreciation schedule affect the after-tax cash flow?
2. What would be the after-tax cash flow if the tax rate were different?
3. How is the gain or loss on sale calculated for tax purposes?
4. Why is accelerated depreciation often used in capital equipment investments?
5. How would selling the equipment before or after 3 years change the calculations?

Tip: Understanding depreciation methods is key for determining the tax impact on asset sales, which directly affects after-tax cash flows.