Net present value: A project costs $3,250,000. The project is expected to generate annual cash flows of $1,225,000 for the next five years. If the company's required rate of return is 10 percent, what is the NPV of this project?

To calculate the Net Present Value (NPV) of the project, we use the NPV formula:

\[
NPV = \sum \frac{CF_t}{(1 + r)^t} - C_0
\]

Where:
- $CF_t$ = Cash flow in year $t$
- $r$ = Discount rate (10% or 0.10)
- $t$ = Time period (years)
- $C_0$ = Initial investment (cost of the project)

In this case:
- Initial investment ($C_0$) = $3,250,000
- Annual cash flows ($CF_t$) = $1,225,000 for 5 years
- Discount rate ($r$) = 10% or 0.10
- Time periods ($t$) = 1, 2, 3, 4, and 5 years

We will calculate the present value (PV) of each annual cash flow and subtract the initial cost to find the NPV.

\[
NPV = \left( \frac{1,225,000}{(1+0.10)^1} + \frac{1,225,000}{(1+0.10)^2} + \frac{1,225,000}{(1+0.10)^3} + \frac{1,225,000}{(1+0.10)^4} + \frac{1,225,000}{(1+0.10)^5} \right) - 3,250,000
\]

Let's calculate that step-by-step.

### 1. First, we compute the present value of each cash flow:
- Year 1: $\frac{1,225,000}{(1.10)^1} = \frac{1,225,000}{1.10} = 1,113,636.36$
- Year 2: $\frac{1,225,000}{(1.10)^2} = \frac{1,225,000}{1.21} = 1,012,396.69$
- Year 3: $\frac{1,225,000}{(1.10)^3} = \frac{1,225,000}{1.331} = 920,360.63$
- Year 4: $\frac{1,225,000}{(1.10)^4} = \frac{1,225,000}{1.4641} = 836,691.48$
- Year 5: $\frac{1,225,000}{(1.10)^5} = \frac{1,225,000}{1.61051} = 760,628.62$

### 2. Now, sum these present values:

\[
PV = 1,113,636.36 + 1,012,396.69 + 920,360.63 + 836,691.48 + 760,628.62 = 4,643,713.78
\]

### 3. Finally, subtract the initial investment of $3,250,000 to get the NPV:

\[
NPV = 4,643,713.78 - 3,250,000 = 1,393,713.78
\]

Thus, the **NPV of the project is $1,393,713.78**.

Would you like further details or have any questions?

Here are five related questions to consider:
1. What would the NPV be if the discount rate were 12% instead of 10%?
2. How would changing the cash flows each year affect the NPV?
3. What is the significance of a positive NPV in project evaluation?
4. How would you calculate the Internal Rate of Return (IRR) for this project?
5. What is the relationship between the discount rate and the risk of a project?

**Tip**: A positive NPV indicates that the project is expected to generate more value than its cost, which makes it a good investment.

Learn how to calculate the Net Present Value (NPV) of a project costing $3,250,000 with expected cash flows of $1,225,000 over five years and a 10% discount rate. This solution breaks down the NPV calculation and applies key finance concepts like discounting cash flows and the time value of money.

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