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Ilana Industries Incorporated needs a new lathe. It can buy a new high-speed lathe for $1 million. The lathe will cost $35,000 per year to run, but it will save the firm $125,000 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 $100,000. The discount rate is 8%, and the corporate tax rate is 21%.

What is the NPV of buying the new lathe?

Note: A negative amount should be indicated by a minus sign. Enter your answer in dollars, not in millions. Do not round intermediate calculations. Round your answer to 2 decimal places.

Answer :

The NPV of buying the new lathe is approximately -$388,442.87.

To calculate the Net Present Value (NPV) of buying the new lathe for Ilana Industries Incorporated, we need to consider the cash flows associated with the lathe over its useful life.

First, let's calculate the annual cash flow generated by the new lathe. The lathe will save the firm $125,000 in labor costs per year, but it will also incur an annual operating cost of $35,000. Therefore, the net annual cash flow is $125,000 - $35,000 = $90,000.

Since the lathe is entitled to 100% bonus depreciation for tax purposes, the entire cost of $1 million can be deducted in the first year. This means that there will be no tax payable on the net annual cash flow for the first year.

For the remaining 9 years, the net annual cash flow of $90,000 will be subject to a 21% corporate tax rate. Therefore, the after-tax cash flow for these years will be $90,000 * (1 - 0.21) = $71,100.

Now, let's calculate the present value of the cash flows. Since the discount rate is 8%, we can use the formula:

PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CF10 / (1 + r)^10,

where PV is the present value, CF1 to CF10 are the cash flows for years 1 to 10, and r is the discount rate.

Using this formula, we can calculate the present value of the cash flows as follows:

PV = $0 + $71,100 / (1 + 0.08)^1 + $71,100 / (1 + 0.08)^2 + ... + $71,100 / (1 + 0.08)^10.

Calculating this sum, we find that the present value of the cash flows is approximately $511,557.13.

Finally, we need to subtract the initial cost of the lathe and add the salvage value at the end of 10 years to calculate the NPV. The NPV is given by:

NPV = PV - Initial cost + Salvage value = $511,557.13 - $1,000,000 + $100,000.

Calculating this, we find that the NPV of buying the new lathe is approximately -$388,442.87.

Note that the negative sign indicates a negative NPV, which means that buying the new lathe is not financially beneficial for Ilana Industries Incorporated.

Therefore, the NPV of buying the new lathe is approximately -$388,442.87.

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