A power plant costs $200,000. This plant will produce an inflow after operating costs of $50,000 a year for 20 years. If the opportunity cost of capital is 15%, what is the NPV of the factory?

To calculate the Net Present Value (NPV) of the power plant, we use the formula for NPV, which is the sum of the present values of all cash inflows and outflows over the project's lifetime. 

The NPV formula is given by:

\[
NPV = \sum_{t=1}^{N} \frac{C_t}{(1 + r)^t} - C_0
\]

Where:
- $ C_t $ = Cash inflow at time $ t $
- $ r $ = Discount rate (opportunity cost of capital)
- $ t $ = Time period
- $ N $ = Total number of periods
- $ C_0 $ = Initial investment

For this problem:
- Initial investment, $ C_0 $ = $200,000
- Annual cash inflow, $ C_t $ = $50,000
- Discount rate, $ r $ = 15% = 0.15
- Number of periods, $ N $ = 20 years

First, we need to calculate the present value of the annuity of $50,000 per year for 20 years at a discount rate of 15%.

The present value of an annuity can be calculated using the formula:

\[
PV = C \times \left( \frac{1 - (1 + r)^{-N}}{r} \right)
\]

Plugging in the values:

\[
PV = 50,000 \times \left( \frac{1 - (1 + 0.15)^{-20}}{0.15} \right)
\]

Let's calculate this step-by-step:

1. Calculate $ (1 + 0.15)^{-20} $:

\[
(1 + 0.15)^{-20} = 0.061818
\]

2. Calculate $ 1 - (1 + 0.15)^{-20} $:

\[
1 - 0.061818 = 0.938182
\]

3. Divide by the discount rate:

\[
\frac{0.938182}{0.15} = 6.254545
\]

4. Multiply by the annual cash inflow:

\[
PV = 50,000 \times 6.254545 = 312,727.27
\]

Now, subtract the initial investment to find the NPV:

\[
NPV = 312,727.27 - 200,000 = 112,727.27
\]

So, the NPV of the power plant is $112,727.27.

Would you like more details or have any questions? Here are some related questions to explore further:

1. What is the significance of a positive NPV in investment decisions?
2. How would the NPV change if the discount rate was different?
3. What if the operating costs changed, how would that affect the NPV?
4. How does the time period affect the NPV calculation?
5. Can you explain the impact of cash flow timing on NPV?
6. What are some limitations of using NPV as a sole decision criterion?
7. How does NPV differ from other investment appraisal methods like IRR or Payback Period?
8. What factors should be considered when choosing the discount rate?

**Tip:** Always consider the time value of money in investment decisions.

Learn how to calculate the Net Present Value (NPV) of a power plant investment costing $200,000, with annual cash inflows of $50,000 for 20 years and a discount rate of 15%. Detailed step-by-step solution provided.

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