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.

-30.52

To find the Net Present Value (NPV) and Profitability Index (PI) of the project, we need to discount the cash flows using the project's cost of capital.

Step 1: Calculate the Discounted Cash Flows (DCF)

DCF year 1 = $800 / (1 + 0.08)^1 = $800 / 1.08 = $740.74
DCF year 2 = $850 / (1 + 0.08)^2 = $850 / 1.1664 = $729.59

Step 2: Calculate the NPV

NPV = Sum of DCF - Initial Investment
= $740.74 + $729.59 - $1,500
= -$29.67

Step 3: Calculate the PI

PI = (Sum of DCF / Initial Investment) + 1
= ($740.74 + $729.59) / $1,500 + 1
= $1,470.33 / $1,500 + 1
= 0.98

Therefore, the NPV of the project is -$29.67 and the PI is 0.98.

To find the Net Present Value (NPV) and Profitability Index (PI) of the project, we need to discount the future cash flows to their present value using the project's cost of capital. The NPV helps measure the profitability of the investment in absolute monetary terms, while the PI represents the relative value of the project.

1. Calculate the present value factor (PVF) for each cash flow using the formula: PVF = 1 / (1 + r)^n, where r is the discount rate (cost of capital) and n is the year of the cash flow.

For year 1:
PVF1 = 1 / (1 + 0.08)^1 = 0.9259

For year 2:
PVF2 = 1 / (1 + 0.08)^2 = 0.8573

2. Calculate the present value (PV) of each cash flow by multiplying the cash flow by its corresponding PVF.

For year 1:
PV1 = $800 * 0.9259 = $740.72

For year 2:
PV2 = $850 * 0.8573 = $729.71

3. Calculate the NPV by subtracting the initial investment cost from the sum of the present values of the cash flows.

NPV = PV1 + PV2 - Initial Cost
= $740.72 + $729.71 - $1,500
= -$29.57 (negative means the project's value is less than the initial investment)

4. Calculate the PI by dividing the present value of the cash inflows by the initial investment cost.

PI = (PV1 + PV2) / Initial Cost
= ($740.72 + $729.71) / $1,500
= 0.9862

Therefore, the NPV of the project is -$29.57, and the PI is 0.9862.