## 1

If, in Year 0, the project required an investment of \$200,000, the simple payback would be 2 years. Yet, when the cash flows are time-valued, the investment would not be recovered until sometime in Year 3. Where as a non-discounted method such as simple payback or ROR would assume the cumulative net cash flow to be \$300,000 at the end of Year 3, the discounted analysis reveals a smaller PV sum of \$248,680.

As indicated by the continually diminishing PVF, when applied over a longer term, for example 10 or 20 years, this gap between discounted and non-discounted cumulative net cash flow widens, showing non-discounted analysis methods to be crude and potentially misleading. Extending this analysis out to 15 years, for example, shows the PV of the cumulative net cash flow to be about \$760,000, or just about half of the non-discounted amount of \$1,500,000. If the initial investment were \$800,000 instead of \$200,000, the simple payback would be 8 years. However, if the useful life of the project were only 15 years, the discounted analysis would show the net annual cash flow to never fully pay back the investment.

The critical value of PV-type analysis is that by the process of discounting, a series of cash flows can be adjusted to determine their actual value in the present. Thus, an investor can view two opportunities, each perhaps with a different life cycle and cash flow shape, and conduct a more objective analysis as to which one, on the basis of the assumptions used, is better.

If cash flows are a fixed uniformed series of equal amounts in each year, the PV is the product of the cumulative PVF for the series and the payment amount. PVFs can be found in standard tables or determined using computer spreadsheet functions. PVF for a series of years can be calculated as:

Using the previous example, the 3-year cumulative PVF is calculated as:

and the PV is:

## Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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