Final answer:
The question involves calculating the NPV for an injection-molding machine purchase and determining if the purchase is justified based on the NPV, which is a financial measure indicating the value of an investment. To compute the NPV, the present value of future revenues and the salvage value at the end of the machine's life are considered, subtracted by the initial investment cost at a discount rate of 12%.
Step-by-step explanation:
The question asks us to calculate the Net Present Value (NPV) for Larson Manufacturing's potential purchase of a new injection-molding machine and to determine whether the purchase would be justified based on the NPV. The initial cost of the machine is $250,000, and there are additional installation costs of $20,000. The machine will increase revenue by $90,000 per year over its five-year life, at which point it is expected to have a salvage value of $75,000.
Steps to Calculate NPV:
- Calculate the present value of the revenue generated by the new machine over the five years.
- Calculate the present value of the salvage value of the machine after five years.
- Subtract the total initial investment from the sum of the present values calculated in steps 1 and 2.
To calculate the present value, we use the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate (12% in this case), and n is the number of years until the payment.
The NPV of the project at an interest rate of 12% is the sum of the present values of the annual revenue and the salvage value minus the initial outlay. If the NPV is positive, then the purchase of the new injection-molding machine would be justified since it would bring a net benefit to Larson Manufacturing.