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Answer :
NPV of buying the new lathe: $539,930.28
To calculate the NPV, we need to consider the initial cost of the lathe, the annual operating cost, the labor cost savings, the salvage value, the discount rate, and the tax rate.
1. Calculate the annual cash flow:
Annual cash flow = labor cost savings - annual operating cost
Annual cash flow = $160,000 - $50,000
Annual cash flow = $110,000
2. Calculate the tax shield on the annual cash flow:
Tax shield = tax rate * annual cash flow
Tax shield = 0.21 * $110,000
Tax shield = $23,100
3. Calculate the net cash flow after tax:
Net cash flow = annual cash flow + tax shield
Net cash flow = $110,000 + $23,100
Net cash flow = $133,100
4. Calculate the present value of the net cash flow for each year:
Present value = net cash flow / (1 + [tex]discount rate)^{year[/tex]
Present value (Year 1) = $133,100 / (1 + 0.10)¹
Present value (Year 1) = $121,000
Present value (Year 2) = $133,100 / (1 + 0.10)²
Present value (Year 2) = $110,000
Present value (Year 3) = $133,100 / (1 + 0.10)³
Present value (Year 3) = $100,000
Continue this calculation for all 10 years.
5. Calculate the present value of the salvage value:
Present value (Salvage value) = $400,000 / (1 + 0.10)¹⁰
Present value (Salvage value) = $148,643.57
6. Calculate the present value of the initial cost:
Present value (Initial cost) = $1,500,000 / (1 + 0.10)⁰
Present value (Initial cost) = $1,500,000
7. Calculate the net present value (NPV):
NPV = sum of all present values - initial cost
NPV = Present value (Year 1) + Present value (Year 2) + ... + Present value (Year 10) + Present value (Salvage value) - Present value (Initial cost)
NPV = $121,000 + $110,000 + $100,000 + ... + Present value (Year 10) + $148,643.57 - $1,500,000
NPV = $539,930.28 (rounded to the nearest cent)
Therefore, the NPV of buying the new lathe is $539,930.28.
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