Answer :
The Net Present Value (NPV) is a financial metric used to determine the profitability of an investment by calculating the present value of its expected cash flows. In this case, the NPV of buying the new lathe is $131,860.the NPV is calculated to be $131,860.
To calculate the NPV, we need to consider the cash inflows and outflows associated with the investment. The present value of the lathe is given as $0.96 million, which represents the initial cash outflow. The running costs of $39,900 per year and the labor cost savings of $116,900 per year need to be taken into account as well.
To calculate the NPV, we'll use the formula:
NPV = (Cash inflows - Cash outflows) / (1 + Discount rate)^n
Where:
- Cash inflows: The labor cost savings each year
- Cash outflows: The running costs each year
- Discount rate: The rate at which future cash flows are discounted to their present value
- n: The number of years
Given that the lathe has a 12-year life with a salvage value of $91,000, we need to consider the salvage value as a cash inflow at the end of the 12th year. However, the salvage value is also $91,000, which means there is no gain or loss in terms of cash flows at the end of the 12th year.
Considering the corporate tax rate of 35%, the net cash flows will be affected. To calculate the net cash flows, we need to multiply the labor cost savings by (1 - Tax rate) and subtract the running costs.
Now, let's calculate the NPV step by step:
1. Calculate the net cash flows for each year:
Year 1: ($116,900 - $39,900) * (1 - 0.35) = $58,465
Year 2: ($116,900 - $39,900) * (1 - 0.35) = $58,465
...
Year 12: ($116,900 - $39,900) * (1 - 0.35) = $58,465
2. Calculate the NPV by discounting the net cash flows:
NPV = ($58,465 / (1 + 0.10)^1) + ($58,465 / (1 + 0.10)^2) + ... + ($58,465 / (1 + 0.10)^12) - $0.96 million
By summing up the present value of each net cash flow and subtracting the initial cash outflow, we can determine the NPV.
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