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Answer :
The NPV of buying the new lathe is approximately $976,934.88.To calculate the NPV (Net Present Value) of buying the new lathe, we need to determine the present value of the cash flows associated with the lathe.
Here are the steps to calculate the NPV:
Step 1: Calculate the annual after-tax cash flow from operating the lathe.
Annual After-Tax Cash Flow = Savings in Labor Costs - Annual Operating Costs
Annual After-Tax Cash Flow = $156,000 - $41,000
Annual After-Tax Cash Flow = $115,000
Step 2: Calculate the present value of the annual after-tax cash flows over 10 years.
Present Value of Annual After-Tax Cash Flows = Annual After-Tax Cash Flow * (1 - Tax Rate) * [1 - (1 + Discount Rate)^(-Number of Years)] / Discount Rate
Present Value of Annual After-Tax Cash Flows = $115,000 * (1 - 0.21) * [1 - (1 + 10%)^(-10)] / 10%
Present Value of Annual After-Tax Cash Flows ≈ $783,579.12
Step 3: Calculate the present value of the salvage value at the end of 10 years.
Present Value of Salvage Value = Salvage Value / (1 + Discount Rate)^Number of Years
Present Value of Salvage Value ≈ $450,000 / (1 + 10%)^10 ≈ $193,355.76
Step 4: Calculate the total present value of cash flows.
Total Present Value of Cash Flows = Present Value of Annual After-Tax Cash Flows + Present Value of Salvage Value
Total Present Value of Cash Flows ≈ $783,579.12 + $193,355.76 ≈ $976,934.88
Step 5: Calculate the initial investment (cost of the lathe) after considering bonus depreciation.
Initial Investment = Cost of Lathe - Bonus Depreciation
Initial Investment = $1,600,000 - $1,600,000 (100%) = $0
Step 6: Calculate the NPV by subtracting the initial investment from the total present value of cash flows.
NPV = Total Present Value of Cash Flows - Initial Investment
NPV ≈ $976,934.88 - $0 ≈ $976,934.88
Therefore, the NPV of buying the new lathe is approximately $976,934.88.
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