Suppose a project has a $2,000,000 net investment and net cash flows (NCFs) of $700,000 annually for 7 years. If the investor's required rate of return is 10%, what is the NPV of this project?
To calculate the Net Present Value (NPV) of a project, we need to discount the net cash flows (NCFs) to their present value and subtract the initial net investment.
The formula for NPV is:
NPV = Σ (NCF / (1 + r)^t) - Initial Investment
Where
- Σ represents the sum of the cash flows,
- NCF is the net cash flow for each period,
- r is the discount rate (required rate of return), and
- t is the time period.
In this case, the net investment is $2,000,000, NCF is $700,000 annually for 7 years, and the required rate of return is 10%.
Let's calculate the NPV step by step:
Step 1: Discount the NCFs to their present value:
Year 1: $700,000 / (1 + 0.10)^1 = $700,000 / 1.10 = $636,363.64 (rounded to 2 decimal places)
Year 2: $700,000 / (1 + 0.10)^2 = $700,000 / 1.21 = $578,512.40
Year 3: $700,000 / (1 + 0.10)^3 = $700,000 / 1.33 = $526,315.79
Year 4: $700,000 / (1 + 0.10)^4 = $700,000 / 1.46 = $479,338.84
Year 5: $700,000 / (1 + 0.10)^5 = $700,000 / 1.61 = $434,426.23
Year 6: $700,000 / (1 + 0.10)^6 = $700,000 / 1.77 = $393,258.43
Year 7: $700,000 / (1 + 0.10)^7 = $700,000 / 1.95 = $358,974.36
Step 2: Sum up the present value of the cash flows:
NPV = $636,363.64 + $578,512.40 + $526,315.79 + $479,338.84 + $434,426.23 + $393,258.43 + $358,974.36 = $3,407,189.69
Step 3: Subtract the initial net investment:
NPV = $3,407,189.69 - $2,000,000 = $1,407,189.69
Therefore, the NPV of this project is $1,407,189.69.