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 calculate the Net Present Value (NPV) and Profitability Index (PI) of a project, you need to follow several steps.
Step 1: Calculate the present value of each cash flow
- Cash flow in year 1: $800
- Cash flow in year 2: $850
To calculate the present value of each cash flow, you need to discount them using the project's cost of capital, which is 8 percent in this case.
The formula to calculate the present value of a cash flow is:
Present Value = Cash Flow / (1 + R)^t
Where:
- R is the discount rate (8% or 0.08 in decimal form)
- t is the time period (year 1 or year 2)
Present Value of Cash Flow in Year 1:
PV1 = $800 / (1 + 0.08)^1
Present Value of Cash Flow in Year 2:
PV2 = $850 / (1 + 0.08)^2
Step 2: Calculate the NPV
The NPV is the sum of the present values of all cash flows minus the initial investment.
NPV = PV1 + PV2 - Initial Investment
In this case, the initial investment is $1,500.
NPV = PV1 + PV2 - $1,500
Step 3: Calculate the PI
The PI is calculated by dividing the sum of the present values of all cash flows by the initial investment.
PI = (PV1 + PV2) / Initial Investment
Now, let's plug in the values and calculate the NPV and PI.
PV1 = $800 / (1 + 0.08)^1 = $741.94
PV2 = $850 / (1 + 0.08)^2 = $744.16
NPV = $741.94 + $744.16 - $1,500 = -$13.90 (rounded to the nearest cent)
PI = ($741.94 + $744.16) / $1,500 = 0.990 (rounded to three decimal places)
Therefore, the NPV of the project is -$13.90 and the PI is 0.990.