Final answer:
To calculate the PI, the present value of future cash inflows is determined using the appropriate formula and then divided by the initial investment. With an initial cost of $45,000 and annual inflows of $11,000 at a 9% discount rate, the PI is found to be approximately 1.10.
Step-by-step explanation:
The student's question revolves around calculating the Project's Profitability Index (PI) using the provided project cash flows and cost of capital. The Profitability Index is calculated by taking the present value of future cash inflows and dividing it by the initial investment.
To do this, we first need to find the present value (PV) of each annual net cash inflow of $11,000 for 7 years at the given cost of capital, which is 9%. Using the Present Value of an Annuity formula, PV = P * [(1 - (1 + r)^-n) / r], where P is the annual cash inflow, r is the discount rate, and n is the number of periods. After calculating the PV of the cash inflows, we divide it by the initial cost of $45,000 to find the PI.
To construct a timeline:
- Year 0 (initial investment): -$45,000
- Year 1-7 (annual cash inflow): $11,000
Using a financial calculator or formula, the total PV of annual inflows is calculated as:
PV = $11,000 * [(1 - (1 + 0.09)^-7) / 0.09] ≈ $11,000 * 4.4859 ≈ $49,345.90
The Profitability Index (PI) can now be calculated:
PI = Total PV of inflows / Initial investment
PI = $49,345.90 / $45,000 ≈ 1.10
Therefore, the Profitability Index of the project is approximately 1.10.