Ilana Industries Incorporated needs a new lathe. It can buy a new high-speed lathe for $1.6 million. The lathe will cost $41,000 per year to run, but it will save the firm $156,000 in labor costs and will be useful for 10 years. Suppose that, for tax purposes, the lathe is entitled to 100% bonus depreciation. At the end of the 10 years, the lathe can be sold for $450,000. The discount rate is 10%, and the corporate tax rate is 21%. What is the NPV of buying the new lathe?

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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