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**Return on Investment Analysis**

Photovoltaic Systems Return on Investment Analysis Incentives • Rebates • Grants • Cost Analysis • Life-Cycle Costs • Value of Money • Annualized Costs • Financial Payback • Incentive Adjustments Arizona Solar Power Society

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**Several types of incentives are available for PV and other renewable-energy systems.**

Many people support the idea of PV and other renewable-energy systems, but assume that these systems are too expensive. Even in cases where the system cost is likely to be recovered, the significant initial costs keep some people from investing in a system. For these reasons, government entities, utilities, and nonprofit organizations sponsor incentives to make renewable energy more affordable. See Figure An incentive is a monetary inducement to invest in a certain type of capital improvement, such as an energy-generating system or energy-conservation measure.

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Tax incentives reduce the amount of tax that must be paid, whether they are tax exemptions or tax credits. Tax incentives are typically categorized as deductions or credits. See Figure Exemptions are fundamentally similar to deductions. When an incentive is offered as a tax deduction, an amount is removed from a taxable value. Since the tax owed is calculated as a percentage, the smaller taxable value results in less tax owed. In contrast, tax credits do not reduce a taxable value. Instead, they cancel a portion of actual taxes owed. Credits may be based on a set dollar amount, a percentage of the cost of the system, or a certain amount per unit of energy production, such as cents per kilowatt-hour.

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Renewable energy certificates (RECs) allow a utility or its customers to claim renewable energy while providing a financial incentive for renewable-energy producers. An owner of a renewable-energy system, such as a PV system or wind farm, receives one REC for every 1000 kWh of electricity produced and exported to the utility grid. See Figure A certifying agency ensures that RECs are allocated accurately and that each is assigned a unique serial number. The REC can then be sold on the open market. Several organizations exist that facilitate this trading. The price of RECs floats like shares of stock and varies depending on supply and demand.

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**A life-cycle cost analysis compares the life-cycle costs of various electricity-supply options.**

When analyzing PV systems against alternate energy sources, a standardized life-cycle cost analysis is used. The life-cycle cost is the total cost of all the expenses incurred over the life of an electricity-generating system. Examples of electricity-generating systems include utility connections, engine generators, wind turbines, and PV systems. A life-cycle cost analysis is a comparison of the life-cycle costs of various electricity-supply options. See Figure For example, a consumer may need to decide between installing a PV-only system with a large array or a hybrid system with a small PV array and a wind turbine. While life-cycle costs are not the only consideration, an analysis comparing the various options will help quantify some of the financial pros and cons that lead to a decision.

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Each system option must meet the same requirements, including the length of time used to calculate life-cycle cost. A length of time must also be chosen for use in the analysis. See Figure The period typically represents the expected lifetime of the system component with the longest life. Again, the shorter-lived system components may require maintenance or replacement to extend their lifetimes to the length of the analysis period, adding costs. Life-cycle cost for PV systems is typically evaluated using a 20- to 30-year period.

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The various types of life-cycle costs occur at different points in the life cycle of a power-generating system. Financial costs included in the total life-cycle cost include initial costs, maintenance costs, energy costs, and repair and replacement costs. These costs vary significantly over the analysis period. See Figure The salvage value of the system at the end of its life is also considered, and is a credit rather than a cost.

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A certain amount of present money is equal to a greater face-value amount of future money. The difference in face value depends on the difference in time. Because the life-cycle cost includes monetary values at the beginning, middle, and end of a system’s lifetime, which can span 20 years or more, it is important to consider how the value of money changes over time. The value of a dollar today is greater than the value of a dollar next year and much greater than the value of a dollar 20 years from now. See Figure This change in the value of money affects the relative values of the various life-cycle costs.

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**The present value of future money falls more quickly with higher discount rates.**

Therefore, $3000 at 10 years from now has the same value as $1842 now. The discount rate can have a significant effect on present values of future costs. See Figure When assessing the present value of many future costs, small differences in the discount rate can add up to significant cost variations, which render a life-cycle cost analysis ineffective. A change of only ±1% in the discount rate would change this amount to $1675 or $2027. If the discount rate is too low, the value of future costs will be exaggerated, but if the discount rate is too high, the value of future costs will be underestimated. Therefore, it is important to choose the discount rate carefully. Local banks are a good source for estimated discount rate information.

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The single present value factor is used to quickly calculate the present value of a single future value. As an alternative to the formula method of determining present value, a simple multiplication factor can be used to determine the present value. The single present value factor is a multiplication factor for determining the present value of a single future cost for a given discount rate and period. The factors are arranged in a table of discount rates against time in years. See Figure The factor for a given rate and period is multiplied by the future value to yield the equivalent present value. For example, the single present value factor for a 5% discount rate at 10 years is Multiplying $3000 by yields $1842.

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Related costs that occur every year are calculated and added together for each year to determine the total present value. Some costs occur in every year, such as fuel costs for generators or the cost of utility electricity. Some types of generating systems may have maintenance costs every year. For example, an engine generator may require periodic oil changes that add up to approximately $100 each year. To determine the present value of these costs with the discount rate formula or the single present value factors would require a separate calculation for each year. The present value of $100 (at a 5% discount rate) in Year 1 is $95, in Year 2 is $91, in Year 3 is $86, in Year 4 is $82, and so on. See Figure All these individual costs are added together to yield the total present value of the recurring cost. If the life-cycle analysis is calculated for 20 years, this method is inconvenient and prone to mistakes.

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The recurring present value factor is used to quickly calculate the present value of a future value recurring for a number of years. Similar to the single present value factor, a simple multiplication factor can be used to easily calculate this recurring cost. The recurring present value factor is a multiplication factor for determining the present value of an annually recurring cost for a given discount rate. These factors are arranged in a table similar to that for the single present value factors and are used in the same way. See Figure For example, the recurring present value factor for $100 every year for 20 years at a 5% discount rate is Therefore, the total present value of this recurring cost is $1250 ($100 × 12.5).

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A life-cycle cost analysis totals the present values of all the life-cycle costs over the length of the analysis period. From this calculation, the analysis is straightforward. The system with the lower life-cycle cost is the better long-term value, assuming all other factors, such as reliability or environmental impact, are equal. See Figure The most common types of life-cycle cost analyses are comparisons between a PV system and either an engine generator or utility electricity.

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The life-cycle cost analysis of a utility connection includes the initial connection costs and annual energy costs. The life-cycle cost of a utility connection is the simplest to calculate. There are no maintenance, repair, or replacement costs to consider. There is also no real salvage value, though in certain cases, a utility connection may add value to a rural home when it is up for sale. The only potential sources of costs for a utility connection are initial connection costs and annual energy costs. See Figure

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**The life-cycle cost analysis of an engine-generator system includes each type of cost.**

The life-cycle cost of an engine-generator system is more complicated and includes each type of cost. See Figure First, the initial costs include the purchase and installation of a 5 kW prime power diesel generator with an auxiliary fuel tank, a 500 Ah battery bank, and a 5 kW inverter. The battery system stores excess energy when the generator is running, which means that the generator runs less often and at a more efficient full load. The total initial costs are $8500.

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**The most significant costs in the life cycle of a PV system are the initial costs.**

The life-cycle cost of a PV system is significantly simpler to determine than for most other systems. There are no energy costs, and maintenance, repair, and replacement costs are minimal. The most significant factor is the initial cost. See Figure A 5 kW PV array with two 2.5 kW inverters and a 1000 Ah battery bank is estimated to cost $30,000, including installation.

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Annualizing costs spreads costs evenly over the operating period, but results in the same total life-cycle cost for a system. This means that an annually recurring cost of $2444 over 20 years has the same total present value as the total life-cycle cost. This can be illustrated in a plot of cumulative annualized costs over the operating period. See Figure In contrast to the actual plot of the life-cycle costs, the cumulative annualized cost plot is a smooth curve representing equal annual costs (in present values) over the entire operating period. The two curves result in the same final life-cycle cost at Year 20.

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The payback point occurs when the cumulative avoided cost of one system matches the total life-cycle cost of another system. For example, consider a PV system that costs $5000, but avoids $500 in costs each year. That is, the alternate power-source option would have cost $500 per year if it was chosen instead, but since it is not needed, the $500 is saved. One might assume that these avoided costs accumulate each year; the total avoided costs would be $1000 in Year 2, $1500 in Year 3, $2000 in Year 4, and so on. If at Year 10, the total avoided cost matches the total system cost, then the payback period is 10 years. See Figure

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The payback point can be determined by comparing the actual life-cycle costs of the various system options. One way to determine the payback point is a comparison of the actual costs accumulating throughout the operating period for the various system options. The payback point is easily seen when the life-cycle costs are tabulated or plotted, but the preparation of these numbers is tedious. The present values of the additional costs for each year and each system must be calculated. Cumulative values are then totaled for each year for all costs up to and including that year. When plotted, the variations between the large initial cost and smaller periodic expenses are observable, resulting in stepped cumulative life-cycle cost plots. See Figure

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The annualized-cost method of determining the payback period is relatively simple, though it may be less accurate than the actual-cost method. An annualized cost for each system option can be used to determine the payback point in a manner similar to actual-cost payback analysis. The advantage is that the calculations are typically simpler, though, because of the assumptions inherent to annualizing, they may be less accurate. The utility connection with the line extension has an annualized cost of $2694 ($36,606 ÷ = $2694). Each year this avoided cost is discounted to its present value. The cumulative avoided cost rises quickly, until it eventually equals the total life-cycle cost of the PV system, which occurs during Year 17. See Figure For the engine-generator system, the payback point occurs even earlier, during Year 12, since its annualized avoided cost is higher at $3514.

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**Incentives affect the total life-cycle cost differently, depending on how and when they are applied.**

These life-cycle cost analyses have neglected incentives, which may have a significant effect on final life-cycle cost. With incentives, the unit cost of PV energy may fall to the point where it is comparable to utility rates. The different types of incentives must be treated differently, however, depending on how they are applied. See Figure

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Copyright © 2009 Pearson Prentice Hall. All rights reserved. Chapter 4 Time Value of Money.

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