Final answer:
The NPV for Liberty Bicycles' new machinery purchase is calculated using the present value of the cash inflows (both tangible and intangible), the salvage value, and subtracting the initial investment. A positive NPV indicates the project adds value to the firm.
Step-by-step explanation:
To calculate the net present value (NPV) for Liberty Bicycles considering the purchase of a new piece of production machinery, we first need to identify the cash flows associated with the investment. The initial investment is $70,000, and the machinery is expected to generate net annual cash inflows of $21,000 for the next five years. Additionally, the machinery has a salvage value of $18,000 after five years. The intangible benefits of $1,800 per year savings in missed work due to increased efficiency should also be considered as part of the cash inflows. Given a discount rate of 10%, we can use the provided present value factors to calculate the NPV.
The present value of the annuity (cash inflows) can be calculated by multiplying the annual cash inflows by the present value of an annuity factor (3.7908). Therefore, the present value of the cash inflows is $21,000 × 3.7908. The present value of the salvage value is calculated by multiplying the salvage value by the present value of 1 at the end of five periods (.6209), which gives us $18,000 × .6209. The total present value of the cash flows is the sum of these two numbers. The NPV is then found by subtracting the initial investment from the total present value of the cash flows.
The NPV calculation will be as follows: NPV = ($21,000 × 3.7908) + ($18,000 × .6209) - $70,000. Once we perform the calculations, we will arrive at the estimated NPV for the machinery purchase decision. Considering the intangible benefits adds an additional $1,800 × 3.7908 to the total present value of cash inflows. The decision to invest in the new machinery should be based on whether the NPV is positive, indicating that the investment is expected to add value to the firm.