Answer :
The NPV of buying the new lathe is $317,007.98.To calculate the NPV (Net Present Value) of buying the new lathe, we need to consider the initial cost, annual savings, salvage value, and the discount rate.
1. Initial cost: The lathe costs $1 million.
2. Annual savings: The lathe will save the firm $123,000 in labor costs every year.
3. Salvage value: The lathe is expected to have a salvage value of $115,000 after 11 years.
4. Discount rate: The discount rate is 5%.
To calculate the NPV, we need to determine the present value of the annual savings and the salvage value. We can use the formula:
NPV = Present value of cash inflows - Present value of cash outflows
1. Present value of cash inflows:
The annual savings of $123,000 for 11 years can be discounted using the discount rate of 5%. Using the present value of an annuity formula, the present value of the annual savings is $985,533.79.
2. Present value of cash outflows:
The initial cost of $1 million can be discounted to its present value using the discount rate of 5%. The present value of the initial cost is $783,526.81.
3. Salvage value:
The salvage value of $115,000 after 11 years is the same as the market value. So there is no need to discount it.
Now, we can calculate the NPV:
NPV = $985,533.79 (present value of cash inflows) - $783,526.81 (present value of cash outflows) + $115,000 (salvage value)
NPV = $317,007.98
Therefore, the NPV of buying the new lathe is $317,007.98.
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