Final answer:
The NPV of the project with a 5% discount rate is $227.39. This is determined by calculating the present value of each period's cash flow and summing those values.
Step-by-step explanation:
To calculate the Net Present Value (NPV) of a project using a discount rate of 5%, we need to find the present value of each cash flow and then sum these values. The cash flows are at Period 0: -$1000, Period 1: $747, Period 2: $367, and Period 3: $212. The formula to calculate the present value of future cash flows is PV = CF / (1 + r)^n, where CF is the cash flow, r is the discount rate, and n is the period number.
-
- Period 0: PV = -$1000 / (1 + 0.05)^0 = -$1000
-
- Period 1: PV = $747 / (1 + 0.05)^1 = $711.43
-
- Period 2: PV = $367 / (1 + 0.05)^2 = $332.38
-
- Period 3: PV = $212 / (1 + 0.05)^3 = $183.58
Now, we sum these values to get the NPV:
NPV = (-$1000) + $711.43 + $332.38 + $183.58 = $227.39
The NPV of the project using a 5% discount rate is $227.39. To determine the value of future cash flows in today's terms, we discount them using the 5% rate. We calculate the present value for each period and add these up. A positive NPV indicates the project may be profitable as it suggests that the projected earnings, adjusted for the time value of money, surpass the initial investment.