Final answer:
The net present value (NPV) of the project is $32,378.85. To calculate the NPV, you need to discount each cash flow to its present value using the project's cost of capital. After discounting all the cash flows, sum up their present values to get the NPV.
Step-by-step explanation:
The net present value (NPV) of a project is the present value of its cash inflows minus the present value of its cash outflows. To calculate the NPV, you need to discount each cash flow to its present value using the project's cost of capital. Here's how you can calculate the NPV:
this formula to the given cash flows and a cost of capital of 9%, you can calculate the NPV of the project.
Discount each cash flow using the formula: PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the cost of capital, and n is the time period.
Sum up the present values of all the cash flows.
The result is the NPV of the project.
Applying this formula to the given cash flows and a cost of capital of 9%, you can calculate the NPV of the project.
Year 0: the present value of the initial cash outflow of $126,750 is -$126,750.
Year 1: the present value of the cash inflow of $41,500 is $41,500 / (1 + 0.09)^1 = $38,135.03.
Year 2: the present value of the cash inflow of $49,500 is $49,500 / (1 + 0.09)^2 = $41,704.69.
Year 3: the present value of the cash inflow of $36,250 is $36,250 / (1 + 0.09)^3 = $28,504.04.
Year 4: the present value of the cash inflow of $47,750 is $47,750 / (1 + 0.09)^4 = $34,472.46.
Year 5: the present value of the cash inflow of $23,500 is $23,500 / (1 + 0.09)^5 = $16,312.63.
Summing up all the present values:
NPV = -$126,750 + $38,135.03 + $41,704.69 + $28,504.04 + $34,472.46 + $16,312.63
= $32,378.85.
Therefore, the NPV of the project is $32,378.85.