Final answer:
The net present value of the project is calculated as $355,481.28 by discounting the annual cash inflows of $103,000 at a 7% cost of capital and subtracting the initial investment of $350,000.
Step-by-step explanation:
The question asks about the Net Present Value (NPV) of a project, which is a concept in finance used to determine the value of a series of future cash flows in terms of today's dollars, after accounting for the initial investment and the cost of capital. To calculate the NPV, we discount each of the future cash inflows back to their present value and then subtract the initial investment.
To solve this problem, we need to use the formula to calculate the present value of each $103,000 cash inflow, which is PV = Cash Inflow / (1 + r)^n, where r is the discount rate (in this case, 7%) and n is the number of years from the present. After we have calculated the present value for each year, we add them together to get the total present value of the cash inflows and then subtract the initial investment to find the NPV.
Let's calculate the present value for each year and then find the net present value:
- Year 1: $103,000 / (1 + 0.07)^1= $96,261.68
- Year 2: $103,000 / (1 + 0.07)^2= $89,964.74
- Year 3: $103,000 / (1 + 0.07)^3= $84,066.78
- Year 4: $103,000 / (1 + 0.07)^4= $78,564.11
- Year 5: $103,000 / (1 + 0.07)^5= $73,444.96
- Year 6: $103,000 / (1 + 0.07)^6= $68,697.19
- Year 7: $103,000 / (1 + 0.07)^7= $64,297.85
- Year 8: $103,000 / (1 + 0.07)^8= $60,183.87
Now, let's sum these present values and subtract the initial investment:
Total Present Value of Cash Inflows = $705,481.28
Net Present Value = Total Present Value of Cash Inflows – Initial Investment
Net Present Value = $705,481.28 – $350,000.00
Net Present Value = $355,481.28
After rounding to two decimal places, the NPV of the project is $355,481.28.