investment requires an initial oulay of 105,000 and will generate cash inflow of 20000 for 11 years. What is the NPV using discount rate of 8%
To calculate the Net Present Value (NPV) of an investment, you need to discount the future cash inflows to their present value and subtract the initial outlay. Here's how you can calculate the NPV using a discount rate of 8% for this investment:
Step 1: Determine the cash inflow for each year.
Since the investment will generate a cash inflow of $20,000 per year for 11 years, you can create a table to represent the cash inflows for each year, as follows:
| Year | Cash Inflow |
|------|-------------|
| 1 | $20,000 |
| 2 | $20,000 |
| 3 | $20,000 |
| 4 | $20,000 |
| 5 | $20,000 |
| 6 | $20,000 |
| 7 | $20,000 |
| 8 | $20,000 |
| 9 | $20,000 |
| 10 | $20,000 |
| 11 | $20,000 |
Step 2: Calculate the present value of each cash inflow.
To calculate the present value of each cash inflow, you need to apply the discount rate of 8% to each year's cash inflow. The formula to calculate the present value of a cash inflow is:
PV = CF / (1 + r)^n
Where:
- PV is the present value of the cash inflow
- CF is the cash inflow for the specific year
- r is the discount rate
- n is the number of years from the present to the cash inflow
Using this formula, calculate the present value for each year's cash inflow and add them up to get the total present value:
PV1 = $20,000 / (1 + 0.08)^1 = $18,518.52
PV2 = $20,000 / (1 + 0.08)^2 = $17,129.63
PV3 = $20,000 / (1 + 0.08)^3 = $15,873.02
PV4 = $20,000 / (1 + 0.08)^4 = $14,739.43
PV5 = $20,000 / (1 + 0.08)^5 = $13,718.49
PV6 = $20,000 / (1 + 0.08)^6 = $12,801.53
PV7 = $20,000 / (1 + 0.08)^7 = $11,981.02
PV8 = $20,000 / (1 + 0.08)^8 = $11,249.55
PV9 = $20,000 / (1 + 0.08)^9 = $10,600.52
PV10 = $20,000 / (1 + 0.08)^10 = $10,028.12
PV11 = $20,000 / (1 + 0.08)^11 = $9,526.95
Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6 + PV7 + PV8 + PV9 + PV10 + PV11
Step 3: Calculate the NPV.
Finally, subtract the initial outlay ($105,000) from the total present value calculated in step 2 to find the NPV:
NPV = Total PV - Initial Outlay
= (PV1 + PV2 + PV3 + PV4 + PV5 + PV6 + PV7 + PV8 + PV9 + PV10 + PV11) - $105,000
By substituting the calculated present values into the equation and subtracting the initial outlay, you can find the NPV of the investment.