To determine whether to buy the project, we need to calculate the Net Present Value (NPV) of the project. The NPV is the difference between the present value of cash inflows and the initial investment. If the NPV is positive, the project should be considered, and if it is negative, the project should be avoided.

Formula for Present Value (PV):

$PV = \frac{C}{(1 + r)^t}$

Where:

• $C$ is the cash flow at time $t$,
• $r$ is the interest rate (18% or 0.18),
• $t$ is the year.

Step 1: Calculate the Present Value of Each Cash Flow

1. Year 1: Cash flow = $21,000 $PV_1 = \frac{21,000}{(1 + 0.18)^1} = \frac{21,000}{1.18} \approx 17,796.61$

2. Year 2: Cash flow = $10,000 $PV_2 = \frac{10,000}{(1 + 0.18)^2} = \frac{10,000}{1.3924} \approx 7,186.19$

3. Year 3: Cash flow = $8,000 $PV_3 = \frac{8,000}{(1 + 0.18)^3} = \frac{8,000}{1.6436} \approx 4,869.88$

Step 2: Calculate the Total Present Value of Cash Flows

$PV_{\text{total}} = PV_1 + PV_2 + PV_3 = 17,796.61 + 7,186.19 + 4,869.88 \approx 29,852.68$

Step 3: Calculate the NPV

Now, subtract the initial investment of $30,000 from the total present value of the cash flows: $NPV = PV_{\text{total}} - \text{Initial Investment} = 29,852.68 - 30,000 \approx -147.32$

Conclusion:

The NPV is negative (-$147.32), which means the project would result in a loss at the given interest rate of 18%. Therefore, you should not buy the project, because it does not generate enough value to cover the initial investment.

Would you like further details or clarification?

Here are a few related questions to explore:

1. How do changes in the interest rate affect the NPV of a project?
2. What is the difference between NPV and Internal Rate of Return (IRR)?
3. How would the NPV change if the initial investment was lower than $30,000?
4. What other investment evaluation methods can be used in addition to NPV?
5. Can the NPV be negative even if cash inflows are positive in all years?

Tip: When analyzing projects, always compare the NPV against the required rate of return. If the NPV is positive, it typically means the project is worth investing in.