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This is the incremental operating cash flow after tax ($30,000 savings in labor costs × .60) for the first year. The incremental cash flow consists of the incremental operating cash flow after tax and the incremental depreciation tax shield.
This is the incremental operating cash flow before tax for the first year. The first year's incremental cash flow consists of the incremental operating cash flow after tax and the incremental depreciation tax shield for the year.
The old machine still has life in it. Its expected useful life is 10 years, but it has been in service for only 5 years. Therefore, it could be used for five more years. Since the question asks for the incremental cash flows for the first year, we must compare the cash flows for operating the old machine with the cash flows for operating the new machine. The difference will be the incremental cash flow. The only cash flow associated with the old machine, if the old machine is kept, is the depreciation tax shield. When we calculate the depreciation tax shield for the incremental cash flow, then, we must use the difference between the annual depreciation on the new machine and the annual depreciation on the old machine. The depreciation on the new machine will be $20,000 per year. The depreciation on the old machine is $5,000 per year. The difference is $15,000 per year. The depreciation tax shield on this difference will be 40% of this $15,000, which is $6,000. The incremental operating cash flow after tax is $18,000 ($30,000 savings in labor costs × .60), and the incremental depreciation tax shield is $6,000 ($15,000 × .40), for a total incremental cash inflow in the first year of $24,000. Note that the question asks only for the incremental cash flows for the first year. The difference between the annual depreciation on the old machine and the annual depreciation on the new machine will be a factor only for the first 5 years of the new machine's life, because the old machine, if kept, would be depreciated for only 5 more years. Beginning with the 6th year, the "difference" between the annual depreciation on the old machine and the annual depreciation on the new machine will be equal to the annual depreciation on the new machine, because the annual depreciation on the old machine will be zero (since the old machine, if kept, would be fully depreciated by Year 6).
This is the incremental operating cash flow before tax for the first year plus the difference between the annual depreciation on the new machine and the annual depreciation on the old machine. The first year's incremental cash flow consists of the incremental operating cash flow after tax and the incremental depreciation tax shield for the first year.