Final answer:
To find the NPV of a project, you must calculate the present value of each cash inflow, sum all present values, and subtract the initial investment. The process involves a series of present value calculations using the discount rate and subtracting the initial investment from that sum. The choice that matches the calculation will be the correct NPV.
Step-by-step explanation:
The subject of the student's question is Net Present Value (NPV), which is a calculation in finance used for evaluating investments by comparing the present value of cash inflows with the initial investment outflows, considering a discount rate. In this problem, we want to calculate the NPV of a project with an initial investment of $200,000, generating $50,000 per year for 6 years, using a 12% discount rate.
To calculate NPV, we follow these steps:
- Calculate the present value (PV) of each annual cash flow by using the formula PV = C / (1 + r)^n, where C is the annual cash flow, r is the discount rate, and n is the year number.
- Sum up all PVs to get the total present value of cash inflows.
- Subtract the initial investment from the total PV of cash inflows to determine the project's NPV.
Thus, Each cash flow of $50,000 must be discounted back to its present value and then summed. For example, the first year's present value would be calculated as $50,000 / (1 + 0.12)^1. After calculating all present values and summing them, we subtract the initial $200,000 investment to get the NPV.
If the NPV is positive, it means the investment is expected to generate more cash than the cost of capital (adjusted for the time value of money). If it is negative, it would indicate that the project is not financially viable under the given conditions. In this case, the student should go through the calculations, compare the figures to the multiple choices provided, and choose the result that matches their calculations.