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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?

Answer :

Therefore, the NPV of buying the new lathe is $40,173.55.

To calculate the Net Present Value (NPV) of buying the new lathe, we need to calculate the present value of the cash flows associated with the purchase and operation of the lathe.

1. Initial investment:

Initial cost = $1,000,000

2. Annual cash flows:

Savings in labor costs = $125,000

Operating cost = -$35,000

3. Salvage value at the end of 10 years:

Salvage value = $100,000

4. Calculate annual cash flows after tax:

Tax savings from depreciation = Initial cost × Tax rate

= $1,000,000 × 21%

= $210,000

Depreciation per year = Initial cost / Useful life

= $1,000,000 / 10

= $100,000

After-tax cash flow = Savings in labor costs - Operating cost - Tax savings from depreciation

= $125,000 - $35,000 - $100,000

= -$10,000

5. Calculate NPV using the discount rate:

NPV = Initial cost + (After-tax cash flow × (1 - Tax rate) × (1 - Tax rate)ᵗ) + (Salvage value / (1 + Discount rate)[tex]^{useful life}[/tex])

NPV = -$1,000,000 + (-$10,000 × (1 - 0.21) × (1 - 0.21)¹ + ($100,000 / (1 + 0.08)¹⁰)

NPV = -$1,000,000 + (-$7,900 × 0.79 + $46,414.55)

NPV = -$1,000,000 + (-$6,241 + $46,414.55)

NPV = -$1,000,000 + $40,173.55

NPV = $40,173.55

The NPV of buying the new lathe is $40,173.55.

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