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

$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - C_0$

Where:

• $CF_t$: Cash flow in year $t$
• $r$: Discount rate (8% or 0.08)
• $t$: Year
• $C_0$: Initial investment ($5000)

Now, calculate each term in the summation:

1. Year 1: $\frac{500}{(1 + 0.08)^1} = \frac{500}{1.08} \approx 462.96$

2. Year 2: $\frac{1200}{(1 + 0.08)^2} = \frac{1200}{1.1664} \approx 1029.59$

3. Year 3: $\frac{2000}{(1 + 0.08)^3} = \frac{2000}{1.259712} \approx 1587.03$

4. Year 4: $\frac{2500}{(1 + 0.08)^4} = \frac{2500}{1.36049} \approx 1837.72$

5. Year 5: $\frac{2000}{(1 + 0.08)^5} = \frac{2000}{1.46933} \approx 1361.63$

Summing the Present Values

$NPV = 462.96 + 1029.59 + 1587.03 + 1837.72 + 1361.63 - 5000$

$NPV \approx 1279.93$

Final Answer:

The Net Present Value (NPV) is approximately $1279.93.

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Related Questions:

1. How does a change in the discount rate affect the NPV?
2. What happens to the NPV if the initial investment is reduced to $4000?
3. How is IRR (Internal Rate of Return) calculated for this project?
4. What is the significance of a positive NPV in investment decisions?
5. How would NPV differ if cash flows were unevenly distributed?

Tip:

The higher the discount rate, the lower the NPV, as future cash flows are discounted more heavily.