Find the NPV and PI of a project that costs $1,500 and returns $800 in year 1 and $850 in year 2. Assume the project’s cost of capital is 8 percent.
To find the Net Present Value (NPV) and Profitability Index (PI) of a project, you need to follow these steps:
Step 1: Calculate the discounted cash flow (DCF) for each year's cash inflow.
DCF = Cash inflow / (1 + Cost of capital)^n
Where n is the number of years.
In this case:
- Year 1 cash inflow = $800
- Year 2 cash inflow = $850
- Cost of capital = 8%
DCF1 = $800 / (1 + 0.08)^1 = $740.74
DCF2 = $850 / (1 + 0.08)^2 = $723.59
Step 2: Calculate the NPV by summing up the discounted cash flows and subtracting the initial investment.
NPV = DCF1 + DCF2 - Initial Investment
In this case:
NPV = $740.74 + $723.59 - $1,500 = -$35.67
The NPV is negative, indicating that the project has a negative present value.
Step 3: Calculate the PI by dividing the present value of future cash flows by the initial investment.
PI = (Present value of cash flows) / Initial Investment
In this case:
PI = ($740.74 + $723.59) / $1,500 = 0.8291
The PI is less than 1, which means the project's present value is less than the initial investment.
In conclusion, the NPV of the project is -$35.67, indicating a negative present value, and the PI is 0.8291, indicating a value less than 1. Therefore, this project may not be considered financially favorable under the given assumptions.