Final answer:
The NPV calculation for an investment project requires discounting future cash inflows back to their present value using a specified discount rate and subtracting the initial investment. The cash inflows are projected to start 15 years from today and are discounted at a 6% cost of capital. Once all inflows are discounted and summed, the initial outlay is subtracted to arrive at the project's NPV.
Step-by-step explanation:
To evaluate the investment project's net present value (NPV), we need to calculate the present value of the future cash inflows and then subtract the initial investment. Since the cash inflows begin 15 years from today, we discount each $42,000 inflow at the cost of capital, which is 6%. The formula for calculating the present value (PV) of each cash inflow is:
PV = Future Cash Inflow / (1 + r)^n
Here, 'r' is the 6% discount rate and 'n' is the number of years from today until the cash inflow is received. Since the first cash inflow is 15 years away, we discount each inflow as if it will be received at the end of the 15th, 16th, 17th, and 18th years respectively.
Using this approach:
- PV year 15 = $42,000 / (1 + 0.06)^15
- PV year 16 = $42,000 / (1 + 0.06)^16
- PV year 17 = $42,000 / (1 + 0.06)^17
- PV year 18 = $42,000 / (1 + 0.06)^18
Adding these present values together gives the total present value of the cash inflows. Deducting the initial investment of $171,000 from this sum results in the project's NPV.
After calculating, if the result is negative, this means that the project's NPV is less than the initial investment and may not be a worthwhile investment.