March 1995 y NREL/TP4625173
A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
Walter Short, Daniel J. Packey, and Thomas Holt
National Renewable Energy Laboratory 1617 Cole Boulevard Golden, Colorado 804013393 A national laboratory of the U.S. Department of Energy Managed by Midwest Research Institute for the U.S. Department of Energy under contract No. DEAC3683CH10093
I
"3L/TB4625173
UC Category 1320
DE95000218
. .......
Walter Short, Daniel J. Packey, and Thomas Holt
National Renewable Energy Laboratory 1617 Cole Boulevard Golden, Colorado 804013393 A national laboratory of the U.S. Department of Energy Managed by Midwest Research Institute under contract No. DEAC3683CH10093 Prepared under Task No. AS026100
March 1995
This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United Sates government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof. Available to DOE and DOE contractors from: Off ice of Scientific and Technical Information (OSTI) P.8. Box 62 Oak Ridge, TN 37831 Prices available by calling (423) 5768401 Available to the public from: National Technical Information Sewice (NTIS) U.S. Department of Commerce 5285 Port Royal Road Springfield, VA 22161 (703) 4874650
t*
3
Printed on paper containing at least 50% wastepaper, including 10% postconsumer waste
Preface
A Manual for the Economic Evaluation of Energy Eflciency and Renewable Energy Technologies provides guidance on economic evaluation approaches, metrics, and levels of detail required, while offering a consistent basis on which analysts can perform analyses using standard assumptions and bases. It not only provides information on the primary economic measures used in economic analyses and the fundamentals of finance but also provides guidance focused on the special considerations required in the economic evaluation of energy efficiency and renewable energy systems.
The Analytic Studies Division (ASD) of the National Renewable Energy Laboratory (NREL) developed this manual for the Office of Planning and Assessment (OPA) in the U.S. Department of Energy (DOE). It is envisioned that this manual will serve as a standard reference on economic evaluation within DOE¡¯S Office of Energy Efficiency and Renewable Energy. Several NREL staff members contributed to this manual through valuable input and review. Outside of NREL, many people provided information for and reviewed drafts of the manual. Among the latter are Fred Abel of the Office of Planning and Assessment at DOE, Geopalachari Ramachandra of the Electric Power Research Institute, Jonathan Koomey of Lawrence Berkeley Laboratory, Lisa Chalstrom of the Iowa Utilities Board, Marshall Wise of Pacific Northwest Laboratory, Peter Bos of Polydyne, Inc., and Rosalie Ruegg of the National Institute of Standards. Their help, especially that of Rosalie Ruegg and Peter Bos, who provided many detailed comments, is very much appreciated. Approved for the National Renewable Energy Laboratory
Thomas D. Bath, Director Analytic Studies Division
Market Analysis Branch Manager and Project Manager
iii
Table of Contents
1
Intxoduction Fundamentals
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1
2
2
2 2 4 5 9 12 14 22 24 26 27
35
Cashmows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . InflationRates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time Points and Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DiscountRates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CostofCapital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Presentvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FixedChargeRate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Financing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Investor Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uncertainty and Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Selection Criteria Guide
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Explanations for the Economic Evaluation Measures Matrix 4 EconomicMeasures
35
39
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NetPresentValue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Total LifeCycle Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 46 Revenue Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Levelized Cost of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AnnudizedValue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Internal Rate of Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Modified Internal Rate of Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 56 SimplePaybackPeriod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discounted Payback Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 58 BenefittoCost Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SavingstoInvestment Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Integrated Resource Planning/DemandSideManagement Ratio Tests . . . . . . . . . . . . . . . . . 62 69 ConsumerLProducer Surplus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Special Considerations for Energy Efficiency and Renewable Energy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sizing a System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Externalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Government Investments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Backup and Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operation and Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacity and Energy Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73 73 73 73 74 74 75 76 77
iv
Table Of (hfltents (Concluded)
Major Repairs and Replacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Salvagevalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . UnequaILifetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Retro~ts ............................................................ Incorporating Electric Utility Rates in an Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
6 7
79 79 79 80 81
83 86
References
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Bibliography
G l o s s a r y
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87
Appendices Appendix A: Selected Inflation Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Appendix B: Escalation (Deescalation) Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B1 C.1 Appendix C: Real Weighted Average Cost of New Capital 19761989 . . . . . . . . . . . . . . . . Appendix D: Amortization Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.1 Appendix E: Monthly and Continuous Discount Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . E.1 Appendix F: Capital Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. 1 Appendix G: Retrofits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 1 Appendix H: Documentation of Evaluation Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . H1
V
List of Figlures
21
Probability density
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28
22 Cumulative distribution
23
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30 32
Probability distribution over quantity Profit forecast frequency chart
24
4 1
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33
51
Levelized cost of energy cash flows Consumer and producer surplus
42
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70
71
a a
43
44
Consumer and producer surplus w i t h additional supply
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. .
I )
Consumer and producer surplus with subsidy price changes
Solar fraction optimization
..
.
.
72
5 1
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75
52 Retrofitscenarios
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81
Qi
List of Tables
21 Office of Management and Budget Recommended Discount Rates . . . . . . . . . . . . . . . . . . . .
6
22 Recommended Discount Rates for Projects Lacking InvestmentSpecific Data
23
............ 9
11
WACC Calculation Table
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24 Preseqtj Value Calculation Table
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13
a x Rates for Corporations as of December 31, 1993 . . . . . . . . . . . . 17 25 Marginal State Income T
26
State Incentives for Solar Technologies
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18
27 DB Depreciation Method 28 29
31
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22 25
a
Amortization Schedule
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Variables for the Example of Deterministic Sensitivity Analysis
.
a
I )
a
.
.
31 36
Overview of Economic Measures Applying to Specific Investment Features and Decisions Calculation of Current DoTZar AfterTax Cash Flow Net Present Value of Current Dollar Cash Flows Constant Dollar AfterTax Cash Flow
..
41 42 43 44
45
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40 41 41 42 43
44
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Net Present Value of Constant Dollar Cash Flows
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Current Dollar TLCC Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Constant Dollar TLCC Evaluation TLCCVariations
46 47
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45
48 AfterTax TLCC Evaluation 49
45 47
53
BeforeTax TlLCC Evaluation
410 AfterTaxIRR
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411 Results of Using IRR as a Sole Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 MIRR versus IRR
54
55 60
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413 Project Size Alternatives 414 Resource Attributes
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64
1 Introduction
This manual is a guide for analyzing the economics of energy efficiency and renewable energy (EE) technologies and projects. It is intended (1) to help analysts determine the appropriate approach or type of analysis and the appropriate level of detail and (2) to assist EE analysts in completing consistent analyses using standard assumptions and bases, when appropriate. Included are analytical techniques that are commonly required for the economic analysis of EE technologies and projects.
The manual consists of six sections: Introduction, Fundamentals, Selection Criteria Guide, Economic Measures, Special Considerations for Conservation and Renewable Energy Systems, and References. A glossary and eight appendices are also included, E a c h section has a brief introductory statement, a presentation of necessary formulae, a discussion, and when appropriate, examples and descriptions of data and data availability.
The objective of an economic analysis is to provide the information needed to make a judgment or a decision. The most complete analysis of an investment in a technology or a project requires the analysis of each year of the life of the investment, taking into account relevant direct costs, indirect and overhead costs, taxes, and returns on investment, plus m y externalities, such as environmental impacts, that are relevant to the decision to be made. However, it is important to consider the purpose and scope of a particular analysis at the outset because this will prescribe the course to follow. The perspective of the analysis is important, often dictating the approach to be used. Also, the ultimate use of the results of an analysis will influence the level of detail undertaken. The decisionmaking criteria of the potential investor must also be considered.
In some cases, it is possible to use shortcuts that reduce the amount of detail needed and permit use of averages rather than detailed yearbyyear calculations. Very gross analpcal approaches may be suitable for instances in which the results are clear or the validity of detailed studies is questionable. For example, the economic value of an industrial conservation investment may be so clear that a complex analysis of annual savings, given the uncertainties of fukre production plans, is not warranted. This manual addresses these types of considerations.
This manual cannot provide an exhaustive and complete exposition of the theory and practical pitfalls of particular economic methods. For example, using this manual for developing a detailed economic analysis of a sitespecific energyrelated project would be difficult. In some cases, references to more extensive resources are provided, but even these may prove insufficient to answer certain detailed questions. This is particularly true when dealing with some of the special circumstances that relate to the application of energy efficiency and renewable energy technologies. A few of these special circumstances are addressed in Section 5 of the manual, Special Considerations for Energy Efficiency and Renewable Energy Systems. Although there may not be a specific right or wrong way or a specific formula for handling some of these cases, the issues are brought to the attention of the analyst.
No analysis will be valid if it is not based on sound and consistent data. If, for example, an EE technology is being evaluated in comparison w i t h a conventional technology, analyses of both technologies must be based on comparable characterizations (the Energy EfSiciency and Renewable Energy Technology Characterizations sets forth the basis for developing valid and consistent technology characterizations) (Carasso 1995). Similarly, the analysis should be conducted on relevant and consistent macroeconomic and microeconomic bases. This manual does not directly address these data input quulity considerations.
1
2 Fundamentals
This section includes an overview of the basic concepts and elements of economic and financial analysis. These fundamentals include cash flows, inflation rates, discount rates, cost of capital (including weighted average cost of capital and marginal cost of capital), present value, taxes and depreciation, fixed charge rates, financing, and risk and uncertainty.
Cash Flows
Introducfion
Cash flows are an integral part of most analyses and are needed to compute the economic measures described later in the manual. It is difficult to explicitly define a cash flow because the type of cash flows used for an analyses will vary, depending on the type of analysis conducted (e.g., aftertax cash flows, beforetax cash flows, incremental cash flows, and so forth).
Cash flows can be thought of in terms of three different activities performed by a company: operating, investing, and financing. Cash flows from operating activities include all revenues captured, minus operating and maintenance expenses, interest paid, and income taxes paid. Investing activity cash flow includes capital expenditures, and financing activity cash flow includes repayment of debt principal and dividends.
Again, the specific type of analyses being performed will dictate the cash flow to be used. In the individual sections of this manual, detail is provided as to which cash flows are appropriate, given the analysis and investor perspective.
Discussion
Great efforts to be precise when describing the timing of costs and benefits in a cash flow series may not be worthwhile in analyses of developing technologies or of deployments projected far into the fuhrre. For example, an economic evaluation of a n investment may cover a 30year span, but even though costs and benefits will occur at different times throughout that time, representing complex cash flows in a more simple conforming pattern (i.e. annually) sacrifices little accuracy in most cases.
Commonly, cash flows occurring within a period are grouped as a lump sum at the beginning, middle, or end of the period. This mama3 assumes the most common practice, which is endoftheperiod cash flows. Most capita3 investment analyses define a "period" as a year (Ruegg and Marshall 1990). As such, compounding or discounting the cash Rows for the analyses can be performed using an m u d discount rate (discussed in the Discount Rates subsection in Section 2).
Inflation Rates
Infroduction
Costs and revenues can be expressed either in "current" dollars or "constant" dollars. Actual cash flows observed in the marketplace are called current dollar cash flows. They represent the actual number of dollars required in the year the cost is incurred. Current dollar cash flows will change over time because of inflation (or deflation). Constant dollar cash flows @ , ) represent the number of dollars that would
2
have been required if the cost w a s paid in the base year ( n ) . Cash flows expressed in current dollars in year m (Fm) can be transformed into constant dollar cash flows in any year n ( F , , ) by removing the effect of inflation (e),
This formula assumes a constant rate of inflation during the mn y e a d
The base year is defined as the year that the analysis is structured around (see the Time PointsPeriod subsection in Section 2). In the base year, constant and current dollar cash flows are the same,
Riscussion
It is important to be aware of inflation when conducting an analysis. It may be necessary to convert a slearn of cash flows from current dollars to constant dollars, or vice versa, using an inflation rate index. There are a number of inflation rate indices (e.g., Gross National Product [GNP], Gross Domestic Product [GDP], Consumer Price Index [CPI], and Producer Price Index [PPI]). Appendix A presents tables of historical inflation indices, including GNP, GDP, CPI, and P P L deflators. The CPI, which measures the average change in prices in a "basket"of goods and services and represents price trends at the retail level, is probably the most widely followed inflation measure. The national CPI is calculated by averaging the price changes of goods included in the basket for 85 separate locations in the nation every month. CPIs are a3so published on a regional, sizeclass, and crossclassification of region and sizeclass basis, and for 29 local areas.
GNP is the measure of output supplied by U.S. labor and property. As of December 1991, the federal government has switched from GNP to GDP as the primary indicator of national production, primarily because nearly all other countries use GDP instead of GNP. GDP is the measure of the national output of goods and services at market prices, or the measure of output attributable to national located factors of production. Both measures represent economywide price trends. The actual levels of GNP and GDP differ very little, but percentage changes sorne~mes vary. Given the federal change, the availability of GNP measures will become more difficult to obtain, and it is recommended that GDP implicit price deflators be used. The implicit price deflator is the measure of the difference between current dollar GDP (or GNP for GNP implicit price deflators) and constant dollar GDP. It is calculated by dividing the current dollar GDP for a period by the constant dollar GDP in the same period. The movements in the GNP and GDP implicit price deflators closely track those of the CPI (U.S. Dept. of Commerce 1992).
The PPI represents price trends at the wholesale level, based on nearly 3100 commodity price series. Though more erratic, patterns in the PPI normally track and foreshadow movements of the CPI, GNP, and GDP indices. Other inflation indices include the Industrial Materials Prices Index, the Dow Jones Commodity Spot Price Index, and the Futures Price Index.
'If infiation rates vary by year and it is important to account for this variation (i.e., an average annual rate will not suffice) the (1 + e)mn portion of the formula would have to be broken down into multiple periods w i t h uniform inflation, i.e., (1 + e)mn would be replaced by (1 + el)mln (1 + e2)m2m' ...... (1 + er)mr(ml).
There is neither a correct nor an incorrect inflation index to use for an analysis. However, it is recommended that the inflation indices used match as closely as possible the work at hand. For example, if the work is general and national in scope, then the GDP deflator is suitable. On the other hand, if the work is more narrowly defined, such as the regional price of electricity, a regional CPI is suitable. The analyst must use judgment when deciding which indices to apply. Sometimes it is necessary to incorporate future estimates o€ inflation in an analysis. The analyst should be aware of the high degree of uncertainty inherent in projected inflation rates and perform sensitivity analysis (discussed in the subsection Uncertainty and Risk in Section 2) using different inflation rates. Projected inflation rates can be obtained fiommany private sector sources; the federal government projects these rates twice a year in presidential administration economic forecasts (OMB 1992).
It is important to note that there may be price changes in particular goods and services that are larger or smaller than changes resulting from general price inflation. See Appendix B far a discussion on escalation.
Time Points and Periods
Time points and periods are crucial factors in an analysis. Time points considered critical to an analysis include the base year, dollar year, and investment year. These are important primarily from a reporting standpoint.
Base YearRex Zero  Year to which aT1 cash flows are converted.
Dollar Year Investment Year
 Year to which base year results are converted and reported (possibly for
comparison purposes with other years).
 Year in which the actual investment occurs.
Important time periods €or the andyst include the investment lifetime (L), the analysis period (N), the depreciation period (M), the finance period (Y), and the levelization period (P). Investment Useful Lifetime

Estimate of a particular investment's useful life. (If not already available through sources such as the EPRP TAG [EPRI December 19911, which provides values for generating technology book lives [investment life, 30 years in most cases], the equipment manufacturer should be contacted.)
Analysis Period Depreciation Period Finance Period Levelization Period
 Period of time for which an evaluation is conducted.  Period of time over which an investment is amortized (usually for tax purposes).

Period of time for which an investment's financing is structured (e.g., a loan is amortized over 30 years).
Period of time used when calculating a levelized cash flow stream.
4
Discussion
In an analysis, ihe time points selected may all be equal (they generally are), different, or in combinations. For example, an independent power producer might wish to evaluate a central receiver plant that would require 2 years to build. The present year could be the base year, 1995 could be the investment year (point in time at which plant would go into service, or inservice date), and 1992 could be the dollar year (year for which material costs are available). Understanding will improve by providing time p i n t information in the reported results of an analysis. If nothing else, it is imperative that the dollar year be reported. Results are meaningless to the reader if values are reported and the dollar year of those results is missing. Results reported in any detail should also include all information pertaining to time period assumptions. Investment lifetime, depreciation periods, and finance periods are all values obtained outside of the analysis but represent €actors to be included in the evaluation. For example, an investment might have an estimated useful life of 30 years, be financed over a 20year period, and be depreciated over 15 years.
The selection of an appropriate analysis period is essential. Many times the analysis period is equd to the investment's life span. However, other factors that should be considered include the investor's time horizon and perspective and the decision to be made (acceptheject or choice among alternatives). The investor's time horizon is often used as the analysis period. For example, the independent power producer evaluating a central receiver plant is planning to sell the plant after 10 years and the central receiver plant under evaluation has an investment life of 30 yeas. In this example, the analysis period should be 10 years. A longer study period, however, should be used for analyses conducted from society's perspective (30 years or more in most cases). Evaluations incorporating acceptheject decisions should use investment life as the analysis period, subject to the constraint of the investor's time horizon. When choosing among alternatives, it is generally agreed that the same study period should be used when evaluating each of the alternatives. Problems can arise if the investment lives of the alternatives differ. More detailed information on projects with unequal lives can be found in the Unequal Lifetimes subsection in Section 5, and in Ruegg & Marshall (1990).
Discount Rates
Time value is the price put on the time that an investor waits for a return on an investment. A dollar received today is worth more than a dollar received tomorrow because the dollar today can be invested to earn interest immediately. Conversely, a dollar received tomorrow is worth less than a dollar received today because the opportunity to earn interest on the dollar is lost. The discount rate acts as a measure of this time value and is central to the calculation of present value. Discount rates are often used to account for the risk inherent in an investment (riskadjusted discount rates are discussed in the Uncertainty and Risk subsection in Section 2). As such, the choice of a discount rate is important to any economic analysis.
Discussion
Analyses can be performed using either current or constant dollar cash flows, but it is important to remain consistent throughout the study. For example, a discount rate is used to calculate the present value of a future payment (present value calculations are addressed in a later section), and a discount rate either includes the effects of inflation (nominal) or excludes inflation (real). The discount rate used in the
5
analysis should be consistent with the form of a92 cash flows. To summarize, red discount rates and constant dollar cash flows exclude inflation, whereas nominal discount rates and current dollars include inflationary effects. A current dollar mdysis requires the use of a nominal discount rate, and a constant dollar analysis requires the use of a real discount rate. Discount rates can be converted from real to nominal, and vice versa, with the following formula:
~
(I + d,) = (1 + dJ(1 + e) = [(l + d,)(l + e)]  1 = [(I + 61,) / (1 + e)]  1 4
an
(23)
Where:
d,,
df
= nominal discount rate = inflation rate.
e
= discount rate in the absence of inflation (red)
For example, given an inflation rate of 6% and a nominal discount rate of lo%, a red discount rate of 3.77% is calculated using the above formula2
Reca3l that the discount rate is a measure of time value. This time value or cost of money is not necessarily the same for all investors. The discount rate will be influenced or determined by a wide variety of factors, such as the investor¡¯s rate of return, risk premium, planning horizon, interest rates, and income and property taxes. Discount rates will vary from state to state, industry to industry, and company to company.
In Circular No. A94 (OMB 1992 revised January 1995), the Office of Management and Budget ( O m ) has established discount rate guidelines for use when evaluating ule costeffectiveness of internal government investments. Appendix C of the circular lists recommended discount rates for short and longterm projects. These rates, presented in Table 22, are based on U.S. Treasury borrowing rates and are updated annually? Analyses of programs with terms different from those presented below may use a linear interpolation. Also, projects with terms longer than 30 years may use the 30year discount rate.
Table 21. Office of Management and Budget Recommended Discount Rates (January 1995February 1996)
I
~~~
3Year
~
5Year
4.5%
7.6%
7Year
4.6% 7.7Oh
10Year
4.0%
30Year
4.9%
8.1%
Real
4.2%
7.3%
Nominal
7.9%
In addition, the federal government annually sets a discount rate for use when evaluating federal projects in which one of the primary purposes of the project includes conservation or renewables. The rate is
2A reasonable approximation is realized by assuming approximate real discount rate is 4. = 10%  6% = 4%
41 = 4 + e. For this example en,
the
30MB Circular A94 also dictates the use of a real discount rate of 7% (based on the average private sector return on investment before taxes) for the evaluation of regulatory programs and public investment; i.e., for investments that benefit the general public (such as a new highway).
6
adjusted annually and is based on longterm Treasury Bond rates averaged over the previous 22 months. This designated discount rate is provided in the annual supplement to NIST Handbook 135, Energy Prices and Discount Factors for LifeQcle Cosl Analysis 1995. If one of the primary purposes of the federal project includes conservation or renewables, the handbook recommends use of a real discount rate of 3.0% and a nominal discount rate of 6.6% (Petersen 1994).
In the private sector, there are no guidelines as to the appropriate discount rate to use for evaluation. As such, sensitivity analysis is recommended w i t h respect to the discount rate. Sensitivity analysis shows the variation in fhe cost or benefit measure as the values of input variables, such as the discount rate change. The subject of sensitivity analysis is covered in the Unce&iinty and Risk subsection in Section 2.
For the commercial and industrial sectors, most experts recommend a discount rate equal to the opportunity cost of capital. The opportunity cost of capital is the rate of return on the best alternative investment available. Unfortunately, these data are not readily available and vary for each investor and investment.
Another measure frequently employed to estimate a discount rate is the cost of capital (the average cost of capital is widely used but the marginal cost of capital is preferred; see the Cost of Capital subsection in Section 2). Here again, the cost of capital varies from one investor and investment to another, which limits its usefulness as a proxy for a general discount rate. However, it is possible to examine the average cost of capital to U.S. industry from 1976 to 1989. As calculated in Appendix C, this average cost of capital (based on historical returns to equity investors md aftertax interest paid on debt) is approximately 5% real (or 7% real be€oretaxes)!
Although these historical averages represent the actual average returns to investors, it should not be assumed that the historical returns represent the ¡°hurdle¡°rate (or discount rate) used by investors to decide whether or not to undertake a specific project. Many investors in the private sector will be seeking a greater than average return. And, of course, many investments carry a higher than average risk, dictating a greater promised return before the project will be undertaken. On the other hand, there are dso many who take a less than average return (i.e., they invest in TBills and lower risk bonds). In the absence of statistical data on discount rates used by industrial, txansportation, and commercial investors for i t h risks similar to those of conservation and renewable energy investments, it is investments w recommended that a real aftertax discount rate of 10% (add in expected inflation to estimate a nominal discount rate) be used within the Office of Energy Efficiency and Renewable Energy for these sectors. O f course, if the analysis concerm a specific investor, the discount rate should be based on the investor¡¯s opportunity cost of capital for investments of similar riskiness.
I
,
,.
In the residential sector, the cost of capital may not accurately represent actual discounting behavior. Residential customers weigh the opportunity cost of capital much greater than financial markets require (EPRI 1987). Recall that the opportunity cost of capital is the rate of return needed to induce investors to invest in a project of similar risk and duration. The residential sector seems to require a much higher rate of return on an investment than financial markets require. Possible explanations for this include uncertainty, short residency period (investment period), availability of capital, income, and noneconomic factors. Perhaps a homeowner does not know how much longer he or she will live at a present address, or a renter does not wish to invest in something that cannot be taken when he or she leaves. Hausman (1979), using data on the purchases of new air conditioners, calculated discount rates that households use
4The aftertax interest rate assumes that the highest marginal tax rate is paid by industry. In reality, however, the actual rate paid is frequently less, making the actual historical real returns to investors, after taxes, somewhere between 5.0% and 7.0%.
7
when purchasing energyefficientunits. His overall real discount rate was approximately 25%. However, when income became a variable, he found considerable fluctuation in the discount rate (i.e., households with an annual income of $10,000 had a red discount rate of 39%, and those with an income o€ $50,000 had a real discount rate of 5%). The circumstances surrounding each residential customer are different, making it difficult to determine an appropriate discount rate for the residential sector. Nonetheless, a discount rate is required. When knowledge of a specific investor is unavailable, a 10% real rate is recommended, with other factors (i.e., noneconomic) considered explicitly.
Because the utility industry is largely regulated, the estimation of discount rates is more formalized and more data exists. Common utility practice is to employ a discount rate equal to the utility¡¯s Weighted Average Cost of Capital (WACC). The calculation of this WACC is explained in some detail in the next section. In the Electric Power Research Institute¡¯s @PH¡¯s) 1991 Technical Assessment Guide @XI June 1993), an aftertax nominal discount rate of 9.2% for investorowned utilities (IEOWs) is suggested in most cases because utilities perform analyses more Q ~ ~ X X in I current dollars than in constant dollars. The analyst should note that the 9.2% nornind discount rate may change, depending on the rate of inflation. In its calculations, EPRL assumed an annual inflation rate of 4.1%, which is a longterm average.
The equivalent real aftertax discount rate is 4.9%. This is significantly less than the 10% suggested for use in the nonutility private sector and is because, as a regulated industry, utilities have little competition in their service territories and their regulated rates help ensure return on investment. Thus, there has historicdly been less risk involved in the utility sector than in other private sectors.
EPRI: also suggests the use of utility beforetax discount rates of 10.8% nominal and 6.4% real. The difference between these and the aftertax discount rates presented previously reflects the fact that debt payments are deductible for income tax purposes. EPRI reports that most utilities employ an aftertax rate. Whether to use a beforetax or an aftertax discount rate will depend on the study itself. This topic is covered in more detail in the Taxes subsection in Section 2, where it is recommended that most EE utility analyses be conducted on an aftertax basis because income taxes can have varying effects on different alternatives.
Because 77% of all U.S. generating capacity is owned by IOUs (EEI October ISSl), the aftertax 9.2% nominal discount rate (or the equivalent, 4.9%real) is recommended for use in the evaluation of El3 technologies within the utility sector. However, the analyst should recognize that significant generating capacity is owned by municipal utilities and rural cooperatives that enjoy special tax status (and may therefore employ a lower nominal discount rate), and by independent power producers (IPPs) whose profits are not regulated (and who may use a higher discount rate that is closer to that of the industxial sector).
Table 22 summarizes discount rates recommended for EE use when investor or investmentspecific data are not available. These discount rates are consistent with those used in the National Energy Strategy released by the DOE in 1993. The development of the nation¡¯s energy options requires investments now that will produce benefits well into the future. As an example, R&D costing billions of dollars may not produce benefits for many years (e.g., 30, 40, 50 years), and these benefits could potentially accrue for hundreds of years thereafter.
As discussed previously, the common approach for evaluating these projects is to discount the costs and benefits to their present values. For projects in which benefits or costs occur well into the future, the discount rate used for the analysis will have a strong impact on the results. As an extreme example, the cost of nuclear waste and contamination may accrue several hundred if not thousands of years from now, and any positive discount rate would allow for even devastating costs to kture generations to be insignificant in terms of present value ( L i d 1982).
8
Table 22. Recommended Discount Rates for Projects Lacking InvestmentSpecific Data
Sector
Government
Industry Transportation Commercial Residential Utilitv
a.
Real Discount Rate (¡±/o)
3.0¡¯
10.0
10.0 18.0
10.0 4.gb
b.
This rate is for energy investment decisions that include conservation or renewable energy alternatives. For other projects, see OMB¡¯s recommended discount rate in Table 21. The beforetax discount rate to use is 6.4%.
The value of such a ¡°social¡±discount rate has been a controversy for decades, and at this point, the experts have not agreed on such a rate. Many have argued that the social rate of discount should be identical to the current private sector discount rates to ensure that public investments with low rates of return would not supplant higherreturn private investments. Others argue that the social rate should be lower than the private rate and equal to the consumption ratethe rate at which consumers are willing to displace consumption now for consumption in the future, A higher rate works against renewables and conservation technologies and generally favors conventional fossil fuel technologies. As such, it is recommended that, if needed, an appropriate social discount rate to use is the government rate outlined in Table 22. However, the analyst should be aware that the rates set by OMB and tihe Federal Energy Management Program could be a function of the current administration¡¯s agenda. For example, an administration favoring less government spending and fewer government projects would push for higher discount rates, thus making it more difficult for projects to pass the costeffectiveness test (Lind 1982).
Discount rates are sometimes adjusted to reflect risk. The subject of riskadjusted discount rates is covered in detail in the Uncertainty and Risk subsection in Section 2.
Cost of Capital
Introducfion
The cost of capital is an important factor in the economic analyses of firms, utilities, and other business entities. The previous section illustsated that cost of capital is frequently used as the discount rate in economic analyses. The cost of capital has to be recovered by the investor to warrant his investment. The price of a good or service to a consumer in a competitive market or in a market subject to utility regulation will include a return roughly equal to the industry¡¯s cost of capital. Higher returns attract increased investment, whereas lower returns discourage investment and lead to inadequate supplies and sources of investment capital.
9
Discussion
Capital is a necessary factor of production and has a cost. Estimating a firm¡¯s cost of capitd involves determining the cost of the various capital components, then applying these costs to the capitalization ratio of the firm to arrive at a WACC. The more common components of capital are debt, preferred stock, and common equity. Calculating the cost of debt and preferred stock is a relatively straightforward procedure. In the case of a regulated utility, common practice is to use the embedded¡¯ cost (actual interest obligation of debt as a percentage of the principal amount outstanding and the annual dividend obligation of preferred stock as a percentage of the net proceeds from the sale of that stock) because the rate base of regulated utilities is embedded (Phillips 1988). EPRI¡¯s 1993 TAG recommends using a beforetax nominal cost of debt of 9.1% and a nominal cost of preferred stock of 8.4% (EPRI June 1993).
Instead of calculating the cost of debt and preferred stock on an embedded basis, a competitive private firm would want to use the marginal cost or the cost of newly issued debt and preferred stock. This is the case because a competitive f i r m should finance projects in such a way that the Marginal Cost of Capital (MCC) is minimized. The f i r m should take on new projects only if the net present values of cash flows are positive when evaluated using the MCC (Weston and Brigham 1981). The cost of new debt can be calculated by dividing the yearly interest amount, after accounting for income tax preferences: by the sales price of the debt, after accounting for any flotation costs? The cost of new preferred stock is calculated by dividing the stated dividend by the sales price of the issue after accounting for flotation costs (Ruegg and Petewsen 1987).
Estimating the cost of equity for a fum is more complicated than calculating the cost of debt and preferred stock. For regulated utilities, EPRI¡¯s TAG 1993 recommends using a nomind cost of equity (common stock) of 13.0%. Three approaches for determining the cost of equity are most commonly used: eamings/price (e/p) ratios, discounted cash flow (DCF) models, and the Capital Asset Pricing Model (CAPM). These methods can be applied to both regulated utilities and competitive firms. The use of e/p ratios and the CAPM is not as predominant as using DCFs and as such, they are not covered in this manual. For more information on the CAPM, see the Uncertainty and Risk subsection in Section 2. Weston covers both models in greater detail (Weston and Brigham 1981).
The equation for calculating the cost of equity (rate of return on common equity) using the DCF model is as €allows:
fk, =
C v p+g
(24
Where: = rate of return on common equity rec = current dividend per share d = current m a r k e t price per share P = expected growth rate of dividends per share. g
¡¯Embedded is defined as average or fully distributed.
61ncome t a x preferences in this instance refers to the tax deductibility of the interest related to debt.
7Flotation costs refer to the costs required when acquiring debt. This may be in the form of commissions paid and other costs.
10
Thus, if the stock of a firm pays a $2 dividend that is expected to grow at an annual rate of 5% and the current market price of the stock is $24, the rate of return on common equity is 13.3%. The overall WACC is based not only on the cost o f the existing capital but also on the structure or distribution of the capital. The general WAC@ formula~on is calculated by:
WACC = r,[C, f (C, + Ps+ D)] + rep[Ps + (C, Where:
Tee
+ Ps+ D)] + (1  T)rd[D + (C, + Ps + D)]
(25)
= rate of return on common equity
C,
P S
D
T
rd
= common stock and corporate retained earnings (Weston and Brigharn 2981) = preferred stock = debt issues
= rate of return on preferred stock = corporate tax rate¡¯
= interest rate paid on debt.
As an example of using the WACC formula, suppose the capital structure of a regulated utility consists of 46% debt at an embedded aftertax nominal cost of 5.6%, 8% preferred stock at an embedded nominal cost of 8.4%, and 46% common equity at a nominal cost of 13.0%. Table 23 shows the WACC calculation.
Table 23. WACC Calculation Table
Security
% of Total
46
3
Cost (¡°3)
5.6¡¯
8.4
Return (¡°3)
2.59 0.67
Common Stock
46
13.0
5.98 WACC = 9.2

¡°The EPRl TAG recommends a nominal beforetax cost of debt of 9.1% and an effective tax rate of 38%. This translates into an aftertax cost of debt of approximately 5.6% because interest is tax deductible; i.e., (1  0.38)(9.1).
In this example, the WACC is 9.2%, which is the WACC recommended by EPRI for use in analyses related to electric utilities. As previously stated, if this had been a private competitive firm, the correct cost components for debt and preferred stock would have been based on the cost of new issues. The WACC value derived would then be called the MCC or the weighted average cost of new capital
The corporate tax rate includes both state and €ederal income tax rates. The effective tax rate, or combined state and federal tax rate, which accounts for the fact that state taxes are deductible on federal returns, can be calculated as: Effective T a x Rate = State Tax Rate + Federal Tax Rate (1  State Tax Rate).
8
(WACNC). As was pointed out in the previous section, Appendix C displays historical WACNC values based on historical returns to equity investors and aftertax interest paid on debt to arrive at an average WACNC of approximately 5% real (or 7% red when the tax deductibility of interest is not accounted for9).
Present Value
introduction
Present value analysis is used to calculate today¡¯s worth of a transaction that will occur in the future to account for changing dollar valuations. In other words, present value is a measure of today¡¯s value of revenues or costs to be incurred in the future (Samuelson and Nordhaus 1985). Because present value is fundamental, it is important to understand the issues surrounding its components and what is being assumed in the present value analysis.
Discussion
The present value of a dollar received or paid in the future can be calculated by multiplying the future cash flow by a present value discount factor, used to discount future cash flows back to the present. The formulas for present value and the present value interest factor are as follows: PV = PVIF, x F,
and
PVFn =
1
(1 + d)¡±
Where:
PV = present value PVWn = present value interest factor = cash flow n years in the future Fn d = annual discount rate.¡±
Therefore:
PV = PVIF, x Fn=
1 (1 + d)¡±
Fn
(27)
¡¯The aftertax interest rate assumes that the highest marginal tax rate is paid by industry. In reality, however, the actual rate paid is frequently less than thh, making the actual historical real returns to investors after taxes somewhere between 5.0% and 7.0%.
¡°Although this manual presents only annual discount rates and cash flows, discount rates and cash flows can be expressed for any period (i.e., monthly). In fact, discount and interest rates can be expressed continuously (see Appendix E: Monthly and Continuous Discount Rates).
12
As an example, aSsurne a discount rate of 5% and a cash i d o w of $1 one y e a Erom now. Using the formula above, the present value is as follows:
PV =
(I + 0 . 0 5 )
x $1 = 0.9524 x $1 = $0.95
.
The $0.95 is approximately the present value of the future cash inflow of $1. Conversely, if $0.95 w a s invested at a 5% interest rate, it would be worth approximately $1 one year from now. This example determines the present value of a cash flow exactly one year in the fblme. The same basic formula can be used to evaluate cash flows in my future period or from now to some point in the future. In this latter case, the present value is a sum of the present value of each future year's cash flow, i.e.,
For example, assume a cash inflow of $1 one year from now and a cash inflow of $5 two years from now at an annual discount rate of 5% The present vdtlue of this inflow is as follows:
PV, =
I x $1 = 0.9524 x $1 = $0.95 (1 + 0 . 0 5 ) '
(210)
PV, =
(1 +
x $5 = 0.9070 x $5 = $4.54
(211)
Once these future cash inflows are converted to present value, they can be added. From the previous calculations, the following table can be constructed:
Table 24. Present Value Calculation Table
Period
1
Cash Flow
$1
PVlF
0.9524
0.9070
Present Value
$ 0.95
$ 4.54
2
$5
PV = $5.49
The example in Table 24 required calculating the present value for each of two future cash flaws. This calculation is necessary when each hture cash flow is uneven or differs in amount. But when fruture cash flows are fixed in size and regularly occur over a specific number of periods, the situation is known as
13
an annuity. For an annuity, mother formula can be used for cdculathg present value. The formula for cdculating the present value of an annuity is as folIowsll:
(2 12)
Where:
PV = present value = cash flow in each of N future years F d = annual discount rate.
For example, assume a cash inflow of $100 per year at the end of each year for the next 5 years at a discount rate of 10%. The following calculation is obtained by applying the formula in Eq. (212):
PV = $100 x
' 0'10)5 ~o.io(i+ 0.10)51
=
$100 x 3.7908 = $379.08
(2 13)
In this example, the present value of the annuity is $379.08.
In these examples, the issue of real or nominal discount rates and dollars w a s not addressed. As was pointed out in the Discount Rates subsection in Section 2, a real discount rate excludes inflation, whereas a nominal value includes inflation. The important thing to remember when calculating present value is to use real discount rates if cash flows are in constant dollars and to use nominal discount rates if cash flows are in current dollars.
Taxes Introduction
Taxes represent additional costs that are no different from, for example, labor and materials costs. As such, dl relevant taxes should be included in an economic analysis. The most complete analysis of an investment in a technology or a project requires the analysis of each year of the life of the investment, taking into account relevant costs, including taxes.
flow should account for federal and state income taxes (if state income taxes are applicable). In most
In most circumstances, cash flow will be the basis for analyzing alternative investments. An aftertax cash cases, analyses should be based on aftertax cash flows. As Stermole points out, the effects of income tax can vary widely from one alternative to another, so it is generally imperative to compare the relative economics of investment alternatives on an aftertax basis to have a valid economic analysis (Stermole 1984).
An illustration of the importance of aftertax analysis is noteworthy here. Suppose a fossil fuel plant with relatively low capita1 costs and high fuel costs is being compared to a solar plant with relatively high capital costs and no fuel costs. Depreciation for tax purposes will be a major factor in this analysis. The "The present value interest factor, [(l + d)N l]/[d(l + d)N], used in the calculation of net present value, is the reciprocal of the uniform capital recovery factor (UCRF).
fuel costs for the fossil fuel plant will be expensed and recovered immediately. However, the solar plant with no fuel cost and higher capital costs will have to wait until capital costs are depreciated to recover costs. Another important factor in aftertax analysis is any energy investment tax credit that might be available to a solar plant. An aftertax analysis will account for depreciation differences and the effects of the investment tax credit and, as such, is key to the analysis in this example. These examples deal with private entities deciding whether to invest in a technology. In these situations, taxes are a red cost that will have an impact on the decision. However, in analyses ftom a societal perspective, taxes are nothing more than transfer payments, with the exception of those designed to correct for externalities.¡¯¡¯ An analysis could indicate that a given technology is beneficial from society¡¯s perspective, but tax distortions prevent that technology from being economically viable from an investor¡¯s viewpoint. Thus, in some instances it may be advantageous to analyze a project¡¯s viability both w i t h and without taxes.
Discussion
The financial treatment of taxes is a very large and complicated subject. The scope of this manual is such that corporate income taxes for the federal and state levels and other relevant taxes, such as property tax and payroll tax, cannot be thoroughly defined or explained through examples. Rather, some important points are brought forth that an analyst should be aware of In performing aftertax analyses of investment alternatives, the analyst should be aware that the relevant tax considerations are what a company considers for tax purposes and not what a company considers for accounting or book purposes. In most cases, what a company does for accounting purposes or annual reports has no relevance to economic analyses. What the company does for tax purposes affects cash flow generation. An equally important point is that for tax calculation purposes, d l dollar d u e s should be expressed in nominal values. This is important because taxes are applied to actud dollar values, and if an analysis were to apply tax rates to dollar values corrected for inflation, the results would be skewed.
It may be necessary to provide more detail for the analysis of a specific project or company. In these cases, there are other factors that should not be overlooked, such as the type of business organization. The three most common types of organizations are the sole proprietorship, the partnership, and the corporation. The tax treatment for these different types of organizations will vary. For EE analyses in which investorspecific data are not available, the use of the highest tax bracket or marginal tax rate is appropriate. This tax rate for corporations is 39%13for corporations with over $100,000 taxable income; for individuals it also varies with income up to 36%. State tax rates will vary. The marginal state tax rates for corporations as of October 1991 are provided in Table 25.
The analyst is advised to use these rates only as a quick guide and to further research state tax rates for a detailed analysis because rates may have changed and the marginal tax rates shown in the table may have different applications. For example, the 9.3% state income tax rate for California is applied to California net income, whereas the 9.3% rate for Arizona is applied to federal taxable income. State and
~~~~~ ~
12
See the subsection Externalities in Section 5 for an explanation of externalities.
a11 examples in this manual use a 34% lax rate, which w a s the marginal corporate rate before August 1993.
13~0te that
15
federal taxes can be combined (to account for the deduction of state taxes on federal returns) to estimate an effective tax rate as ~ o I I o w s ~ ~ : Effective Tax Rate = State Tax Rate + Federal Tax Rate(1  State Tax Rate)
(2 14)
The analyst may also need to factor in special tax considerations that may apply to the analysis, such as energy tax credits, capital gains and losses, depreciable assets, net operating loss carrybacks and carryovers, dividends, interest deductions, and installment tax payments. Weston and Brigham (198 I) cover these subjects in more detail in Managerial Finance. Energy tax credits and depreciation are important components of the tax issue and warrant special attention. These subjects are covered in the next two sections.
Renewable Energy Tax Credits
Energy tax credits for technologies such as renewables can enhance aftertax cash flow and promote investment. An energy investment tax credit is an immediate reduction in income taxes equal to a percentage of the installed cost of a new investment. The tax code mandates that when an energy tax credit is taken, the depreciable base (capital sum to be recovered by depreciation) of the property for which the credit was taken must be reduced by 50% of the amount of the tax credit. Another key provision of the tax code allows for depreciation to be carried through to other businesses owned by that specific firm. This is important because income is usually not very large in the early years of renewable projects.
The Energy Policy Act (EPACT) of 1992 includes a 10% tax credit applicable to solar and geothermal property used for the generation of electricity; however, public utilities are not eligible for this tax credit (CCH 1992). This tax credit was available prior to the EPACT as well, but EPACT extended it indefinitely. EPACT also includes a production tax credit applicable to wind systems and dedicated biomass (crops grown specifically for energy production) systems that generate electricity. This credit provides a 10year, 1.5 cent/kWh production tax credit.
State governments may also offer energy tax credits that are applicable to renewables when calculating state income taxes. State energy tax credits may vary considerably fiom those of the federal government¡¯s. Also, some states have property tax exemption laws that apply to renewable energy projects. The analyst should research the applicable federal and state energy tax credit rules at the onset of an analysis to determine appropriate levels, applicability, and special rules that may apply. When applying a tax credit in an analysis, the analyst should be cautious because tax credits usually apply only to specific costs and not to the total cost of the project. For instance, federal investment tax credit rules do not allow credits to apply to transmission costs. States may have limitations as well. It is recommended that the analyst be certain of the costs the credits may be applied to. Table 26 provides a summary of state tax credits and other financial incentives for solar technologies. An explicit definition of solar technologies is not provided because the table is not comprehensive. For example, a state may provide incentives for residential photovoltaics but not for utility solarthermal systems. Because of these circumstances, the table should only be used for general information. The analyst should research further to identify more specific incentives.
140neimplication of using an effective tax rate that includes both federal and state income tax is that the state depreciation rules are assumed to be the same as the federal depreciation rules.
16
Table 25. Marginal State Income Tax Rates for Corporations as of December 31, 1993 Marginal tax rate ("!) Marginal tax rate (YO)
6.75 7.75
State
.
State
Montana Nebraska Nevada New Hampshire

a.5
7.25
New Jersey
New Mexico New York North Carolina North Dakota Ohio
0 klahoma
7.6
9.0
7.75
10.5
8.9 6.0
6.6
Oregon
Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming
10.5
9.0
5.0
6.0
5.0 8.25
6.0
9.0
7.9

Table 26. State Incentives for Solar Technologies
I
Grant Other
7 I
+ + 9 , ,
Income Tax
Accel. Deprec. Permit Fee
I
I
t
I
X
Accel, Deprec.
Wisconsin Wyoming
TOTALS: 28
X
X
I
7
6
16
4
9
Arnei c a iI Solar Energy
In some cases, it may be that taxes owed are less than the amount of the tax credit. The federal government will allow the company to carry the unused portion of the credit forward to the following year (carryover). For example, suppose a company invests in a solar technology to sell electricity to the grid. The initial investment is $2 million. After the first year of operation, the company owes federal income taxes in the amount of $150,000. The tax credit allows .a reduction in taxes owed in the first year of operation equal to 10% of the initial investment cost, or $200,000. Thus, taxes owed are reduced to a negative $50,000,which could be carried over to the following year. However, these rules may not apply at the state level.
Qepreciation
It is difficult to talk about income taxes without talking about depreciation. For tax purposes, depreciation is a means of recovering, through an income tax deduction, the cost of property used in a bade or business or of property held for the production of income (land is not depreciable). The capital sum to be recovered by depreciation is the "depreciable base," which when adjusted annually by the amount depreciable, becomes the "adjusted base." It is a bookkeeping entry and does not involve the outlay of cash; nor does it involve the actual deterioration of the physical asset. If federal investment tax credits are available, the depreciable base for federal tax purposes must be decreased by half of the tax credit. Internal Revenue Service (IRS) rules for depreciation have gone through changes over the last couple of decades, the most recent of which w a s the 1986 T a x Reform Act. Given the complicated nature of the subject, only the current tax rules (i.e., enacted w i t h the 1986 T a x Reform Act) are reviewed in this manual. The IRS rules should be revisited often to assure that the rules reviewed here are still in practice. It is also important to note that only the current federal rules are discussed. If an analysis requires more accuracy or detail, state depreciation rules should be examined. Another important point is that given the nature of depreciation, annual depreciationallowances are always calculated in current dollars and as such, a nominal discount rate should be used when discounting depreciation cash flows. The Modified Accelerated Cost Recovery System (MACRS) is the name given to the federal tax rules for recovering costs through depreciation. MACRS rules apply to most tangible property placed in service after 1986. MACRS consists of two systems, the General Depreciation System (GDS) and the Alternative Depreciation System (ADS). MACRS provides the following ways to depreciate property:
.
Both the 200% and 150% declining balance (DB) methods over a GDS recovery period The 150% DB method over an ADS recovery period The straight line (defined later) method over an ADS or GDS recovery period.
The depreciation method used depends on the system used (GDS or ADS) and the class and type of property. The major differences between GDS and ADS are the recovery period and method of depreciation used to figure the deduction. The GDS is most commonly used and is the recommended system for EE analysts because it permits use of the declining balance method over a shorter recovery period, resulting in a greater deduction in the earlier years (IRS 1993). The ADS is used when it is desirable to extend an asset's depreciation period. For ADS the straight line method is used over an A D S recovery period. For example, consider a business in which taxable revenue is expected to be greater in future years than in earlier years. In this case, a greater deduction in the earlier years is not as beneficial as an extended depreciation period. The straight line (SL) anmud depreciation method is calculated using the following formula:
D, = (C,  NSV) / N
(2 15)
19
Where:
Dn C, NSV N
= annual depreciation allowance for year n = original cost of the capital investment
= net salvage value (i.e., the estimated salvage value of property, less the cost of removal) = depreciation period.¡±
However, it is important to note that the previous formula applies only when the SL method is used independently throughout the entire recovery period of an asset. When using the DB depreciation method, the IRS rules require that SL depreciation be calculated in addition to DB and that the annual depreciation allowance switches to the SL method in the year in which SE provides a larger allowance than that of DB. For the DB method, the annual depreciation allowance is not constant; consequently, the asset¡¯s depreciable base must be recalculated in each recovery year to properly determine the new SL depreciation allowance. Therefore, the following formula must be used to calculate the SL depreciation allowance when testing for SL crossover using the DB method:
(2 16)
Where:
D, B,, N
= annual depreciation allowance for year n
= remaining book value of the asset = depreciation period
= analysis year.
n
The DB depreciation method can be applied using either a 200% or 150%declining balance percentage. Property cataloged as 3, 5, 7, or 10year class property is depreciated using the 200% method; property cataloged as 15 or 20year class property is depreciated using the 150% method. Salvage value is not allowed or considered when calculating depreciation using DB. The depreciation allowance for any year n, using the DB method, can be computed with the following formula (Au and Au 1983):
(217)
Where:
D,
r
n
B,,
= annual depreciation allowance for year n = annual percentage rate of depreciation applied to the remaining book value, [(2 or 1.5, depending on whether the DB method is 200% or 150%)+ N],
= number of years the asset will be depreciated (depreciation period) = remaining book value of the asset.
It is important to note that these depreciation formulas, as well as all of the examples that follow, assume that the IRS allows for a full year of depreciation in the year in which the property is placed in service. For simplicity, this assumption is made in the examples presented in this manual, but in actual practice, this assumption is not valid. For the first year of operation, the IRS actually allows for either onehalf year of depreciation (halfyear convention) or an alternative amount based on which quarter of the year
15A useful life is the estimated life of the investment before it must be replaced. The depreciation period is the number of years allowed to recover the cost of an investment through depreciation. The analysis period is the number of years included in an analysis.
/
20
the property was placed in service (midquarter convention). The midquarter convention is only allowed if more than 40% of the value of dl assets placed in service during the year were done so during the last quarter of the year. The IRS has similar rules for the year in which a property is taken out of service before klly depreciated. If an analysis requires more accuracy or detail than what is provided in this manual, the IRS rules should be examined more c~osdy.
In addition to the depreciation method, the depreciation period for the related technology or property must be determined. The IRS provides guidelines or recommended recovery periods for many different types of properties (see IRS Publication 534 [IRS 1993]), Examples of recommended recovery periods using GDS methods include:
Alternative energy property (nonutility generators)  5 years Alternative energy property (public utility generators)  7 years Nuclear production plant  15 years Nuclear fuel assemblies  5 years Hydro production plant  20 years Steam production plant  20 years Combustion turbine production plant  15 years Transmission and distribution plant  20 years Nonresidential red property  31.5 years. Recommended recovery periods using ADS methods include: Alternative energy property (nonutility generators)  12 years Nuclear production plant  20 years Nuclear fuel assemblies  5 years Hydro production plant  50 years Steam production plant  28 years Combustion turbine production plant  20 years Transmission and distribution plant  20 years Nonresidential real property  40 years. The class life of property is determined by referring to Appendix B of IRS Publication 534 (IRS 1993). If an item is not described in the publication, such item should be depreciated using a 7year recovery period under GDS, or a 12year recovery period under ADS. Also, note that a particular project can have equipment with different depreciation schedules (such as in the case of the nuclear project). If there are any questions regarding the appropriate class life of an investment or a component of that investment, the IRS should be contacted. Table 27 illustrates the 200% DB depreciation method. This example assumes a nonredestate capital asset is purchased that has a 7year life and a book value of $10,000, with no salvage value. The asset is depreciated at the 200% DB rate until the annual depreciation values using DB versus SL crossover in year five. At that time, the depreciation method switches from the DB method to the SL method and the remaining value of the asset is depreciated at the flat rate of $867.69 per year. The last column in the table calculates the present value of accumulated depreciation (PVDEP), assuming an investor nominal discount rate of 12%. After 7 years, the present value is only $7,202. The difference between the $10,000 original investment and the present value of depreciation ($7,202) represents that portion of the investment that is, in effect, unavailable to the investor as a tax deduction because of the time value of money. Shorter depreciation periods are thus preferred by most investors. Clearly, there are noticeable tax benefits for using DB depreciation rather than SL depreciation. For example, suppose a machine is purchased for $100,000 and has no expected salvage value and is to be
21
depreciated over a 10year period. The cost of the machine must be charged against production over the machine's depreciation period. Using the formulas for SL and DB, firstyear depreciation can be calculated as follows:
Table 27. DB Depreciation Method Present Value Accumulated Depreciation
Year
Net Book Value
Decfining Balance Depreciation
Test ~f
se
Method
Depreciation
Accumulated Depreciation
SL: D, = $100,000 + 10 = $10,000
DB:D, = $100,000 x (2 + 10) = $20,000.
(218)
(219)
less in the first year. Faster depreciation is preferred because an aftertax dollar earned today is workh more than an aftertax dollar earned tomorrow (i.e., the time value of money).
By using the DB depreciation method, the amount of allowable depreciation is $10,000 more in the first yew than it would have been had the SL depreciation method been used. Thus, taxable income is $10,000
Fixed Charge Rate
In froduction
A fixed charge rate (FCR) allows for quick determinations of the amount of revenue needed to cover investment costs for simple, straightforward investments. The FCR is defined as the amount of revenue per dollar of investment that must be collected annually from customers to pay the carrying charges on that investment (EPRI May 1987). Carrying charges include return on debt and equity, income and property tax, book depreciation, and insurance. For example, an FCR multiplied by the total capital requirement of a capital investment will calculate the revenue needed each year to support the investment. See Appendix F for a detailed explanation of total capital requirements.
22
Discussion
Use of a fixed charge rate does not allow for explicit consideration of projectspecific financing. However, the discount rate can implicitly incorporate debt financing through the use of a weighted average cost of capital to a firm, as discussed earlier.
To capture tax considerations of the investor and the investment, the formula for calculathg the annual fixed charge rate can take one of three forms: a notax investment scenario, a costaftertaxdeductions investment scenario, or a beforetaxrevenuerequked investment scenario. The formulas are as follows:
No Tax:
FCR = ucw
+ PI+ p2
(220)
Cost After Tux Deductions:
Before Tux Revenue Required:
FCR =
n =1
(1  T)
(222)
fixed charge rate uniform capital recovery factor defined as
1/c 1/(1 + dx)¡±
N
where the discount rate 4 = d, or d,, depending on whether it is desired to express the annual carrying charges in real or in nominal dollars depreciation period in years fraction of depreciation base (depreciable fraction of capital costs) analysis year marginal income tax rate of the investor (state and federal) fraction of depreciable base that can be depreciated in year n nominal discount rate (must be used in conjunction w i t h the nominal depreciation allowance) analysis period tax credit annual insurance cost as a percentage of total plant investment in red or nominal dollars, depending on the form of the UCRF other taxes (i.e., property taxes) paid annually as a percentage of total plant investment in real or nominal dollars, depending on the form of the UCRF (Blum, Schweizer, and Morse 1989).
The notax formula is applicable to the following investors and investments: owneroccupied residences, nonprofit organizations, the government, and so forth. The costaftertaxdeductions formula is applicable
23
to forprofit firms with profits fiom other activities against which the tax deductions can be applied. The aftertax cost is most relevant to energysaving investments in which no energy product is produced for sale to customers. The beforetaxrequiredrevenue formula is applicable to profitseeking firms that desire to know how much they will have to charge for the energy they are supplying in order to recover their costs, as well as make their desired return (as defined by the discount rate used in the fixedcharge rate calculation). Any comparison between two investments should be conducted on the same tax basis, i.e., both with no tax, or both on a costaftertax basis, or both on a beforetaxrevenuerequired basis. Note that the distinction between the formulas for the costaftertaxdeductions and the requiredrevenue formula is simply the division of the former by the marginal income tax rate. It is also interesting to note that the notax formula and requiredrevenue formula would be identical if there were no tax credit and if the present value of depreciation [b V$(l + were equal to unity (i.e., if it were d, = 0 or Vo = 1).
a>"]
The fixed charge rate can be calculated on either ;e real or nominal basis by using a red or nominal discount rate in the uniform capital recovery factor. Regardless of which is used for the UCRF portion of the FCR, the discount rate employed to calculate the present value of depreciation in the FCR calculation should be a nominal discount rate because depreciation in each year is calculated in nominal dollars.
Financing Introduction
Financial markets provide the mechanism through which firms obtain funding. Sources of funding can come from commercial banks, savings and loans, finance companies, insurance companies, pension funds, investment funds, investment bankers, brokers, dealers, households, governments, and other business firms. Funds are raised fiom these external sources and allocated to specific projects and assets. The cash flow cycle i s then managed, and the finds are eventually returned to the financial sources (Weston and Brigham 1981).
A financial transaction results in the creation of both an asset and a liability. The creation and transfer of these assets and liabilities form financial markets. These financial transfers can be in the form of loans, bonds, common stock, and preferred stock. When the obligations bought and sold have a maturity of less than 1 year, they are known as money markets, when the maturities are more than 1 year, they are known as capital markets.
It is important for the analyst to understand the two forms of financing: project specific and corporate. Projectspecific financing can be defined as the arrangement of debt, equity, and credit enhancement for the construction or refinancing of a particular facility in a capitalintensive industry where lenders base credit appraisals on the projected revenues from the facility rather than on the assets or credit of the promoter of the facility. This financing relies on the assets of the facility, including revenueproducing contracts and cash flow, as collateral for the debt (") 1992). In contrast, internal or equity financing (corporate financing) can be characterized by the use of corporate credit and the general assets of the corporation as the basis for credit and collateral. Unlike projectspecific financing, it is not tied to any specific projects.
Discussion
Financing is very much related to portfolio analysis and risk. A company wishes to have the optimum portfolio of financial assets and liabilities. In other words, it does not wish to obtain 100%of financing
24
through debt or the issue of stock. A capital stmcture weighted heavily towards one end or the other could be too risky. A typical utility has a capital structure made up of about 50% longterm debt, 45% common stock, and 5% preferred stock. Different forms of financing give rise to various risk levels. For instance, debt is a fixed charge and if eamings fluctuate, the firm's ability to make the obligated payments may be constrained. Debt is also a longterm c o d t m e n t with a fixed maturity and is risky because the expectations and plans for the firm over the long run may change. On the other hand, debt is cost limited, and the cost of debt is normally lower than that of common stock. Also, the interest associated with debt financing is tax deductible.
Forms of longterm debt include bonds, mortgages, and debentures. A bond is a longterm promissory note. Usually these notes are issued in denominations of $1,000. Bonds are payable in full at the end of their stated life. For example, the purchaser of a 10year $1,000 bond with a stated coupon rate of 6% paid annually will receive $60 per year through year ten and receive $1,000 for redemption of the bond at the end of year ten. Company assets are normally pledged as security for bonds issued. A debenture, on the other hand, is also a longterm bond but it Is unsecured (no lien on specific property of the company as collateral) (Weston and Brigham 1981).
A mortgage is a pledge of company property as security for a loan. Most mortgage loans, or term loans, are granted as uniform payment loans, which are amortized in most cases. Amortization provides a gradual uniform stream of repayment, which safeguards both the lender and the borrower. For example, suppose a business borrows $10,000 at 10% compounded annually to be repaid in 5 years. The annual payment due to the lender can be calculated by multiplying the uniform capital recovery factor
UCRF = [d(l
+ d)n]/[(l + d)"  11
(2 18)
by the amount borrowed. In this example, UCRF equals
[o.i(i + 0.1)~]/[(1 + 0.1)~  11 = 0.2638
(219)
which when multiplied by the $10,000 borrowed gives a uniform annual payment to the lender of $2,637.97. Table 28 illustrates the amortization schedule for this example.
Table 28. Amortization Schedule
Year
0
(1) Annual Payment (I x UCRF)
(3)
(2) Interest (d x COI.4"'"))
Repayment of Principal (Col. I COI. 2)

(4) Principal Balance (Col. 4("4  Col. 3)
$ 10,000.00
I
2
$ 2,637.97
$ 1,000.00
$ 1,637.97
8,362.03
2,637.97 2,63 7.97 2,637.97 2,637.97
$ 13,189.87
836.20 656.03 457.83
1,801.77 1,981.95 2,180.14 2,398.1 6
$ 10,000.00
6,560.25
3
4
4,578.30
2,398.1 6
0.00
5
Totals
239.82
$ 3,189.87
25
Appendix D provides formulas for calculating the portion of principal in each payment, the portion of interest in each payment, and the principal aemaining in each period. Common stock does not include an obligated fixed annual charge and carries no fixed maturity dates. Also, common stock can be sold more easily than debt because it is appealing to investors given the fact that common stock usually offers higher returns than that of debt and represents ownership in the company. With common stock there is no legal obligation to pay dividends. However, common stock extends ownership and voting rights as well as a share in income. Also, the cost of underwriting and distributing common stock (flotation costs) is usually higher than both debt and preferred stock. Preferred stock, like common stock, does not include an obligated fixed annual charge and carries no fixed maturity dates. Preferred stock owners may not participate in voting and do not get equal participation of earnings; however, they do receive any dividends before common stock holders do. Preferred stock, on the other hand, must be sold on a higher yield than debt. Dividends associated with preferred stock are not tax deductible, making their cost differentid great in comparison with debt. These are only a few of the advantages and disadvantages of the different forms of financing. The financial manager must weigh these differences to make decisions about the optimal mix of financing for the firm. In an economic analysis, financing should be considered only if it will make a difference when comparing alternatives. For instance, if the terms of financing are identical for the comparison of two alternative investments, then financing makes no difference and should not be included. On the other hand, if an investor wants to construct a plant and lowinterest rate financing is available for only the solar plant but not for a conventional alternative, then financing is a critical part of the comparison and must be included. Financing must also be included in an analysis of cash flow requirements. When financing is included in an analysis, then annual cash flows must be used to compute most economic measures such as net present value (NPV), return on investment (ROI), and lifecycle cost &CC). The simplifying assumptions of the FCR, as expressed earlier, are not appropriate when projectspecific financing is included.
Investor Perspective
The economic viability of an investment frequently will be different for different investors. For example, a demandside management investment by a utility will be viewed differently by the utility, the customer receiving the demandside system, customers not receiving systems, and the utility stockholders. Investor perspective refers to this difference in viewpoints.
Discussion
Although the differences among investors often seems intuitive, there are several points that deserve explicit mention:
An investment may be economical fkom the point of view of one investor or stakeholder but not from that of another.
In any comparison of alternative investments, each alternative should be evaluated from the same perspective. For example, a commercial firm¡¯s levelized cost of energy (electricity) saved (after accounting for tax deductions) through an investment in a heat pump for space conditioning should not
26
be compared directly to the beforetax cost of electric power to the firm. For a homeowner investor, this beforetdaftertax issue is not relevant. It is perfectly legitimate to evaluate an investment from several gerspeceives. A municipal utility might calculate both the required revenue associated with a new distribution feeder line and the social costhenefit ratio of the same line.
Not only are the tax concerns and data different mong investors, many other data also vary with the investor and the nature of the investment (e.g., discount rates, interest rates available on financing, energy supply costs, and so forth).
Different measures of economic viability are used by different investors and for different types of investments. Utilities, for example, will typically compare and evaluate alternative generation systems by calculating the revenue required to recoup the costs of the systems, whereas homeowners might use simple payback calculations. Measures used will also vary within a market sector. An independent power producer may evaluate an investment through the internall rate of return, as opposed to a utility¡¯s evaluation through the required revenue measure. Considerations such as taxes, data variations, and different measures for evaluation are discussed in more detail in the sections that follow.
Uncertainty and Risk
lntroduction
Uncertainty refers to the analyst¡¯s sfate of information about a variable or parameter of interest, specifically when the quantity cannot be known perfectly. Uncertainty is often, but not always, associated with variables that will be revealed at a later time, such as the outcome of an experiment or next year¡¯s oil price.
A closely related concept is variability. Variability refers to a parameter varying across a group or population. For example, there is significant variability in retail electricity prices by region in the United States. A parameter with variability may or may not be uncertain. For example, current retail electricity prices are variable but certain, whereas future electricity prices are both variable and uncertain.
A third concept is risk A general definition of risk is the uncertainty associated with a key value criterion. An example of risk is the uncertainty in the net present value of a project. The relationship of a specified risk to the uncertainties and variabilities in project economics can be explored using the procedures discussed next.
Discussion
Applications of Uncertainty Analysis
Uncertainty arises in two contexts in economic analysis. It can arise when performing primary economic evaluations, such as an accepureject decision of investing in a new technology; it can also arise when trying to predict the economic decisions of others such as predicting how consumers will react to an increase in electricity prices.
27
Because the results of economic evaluations are frequently used in planning and policy making, significant uncertainties must be identified and treated explicitly. The most internally consistent (i.e., the uncertainty in specific variables is specifically addressed) and complete methodology to support such decision making under uncertainty is decision analysis, as described, for example, by Howard (Howard 1977; Howard 1990). Although a complete discussion of decision analysis is beyond the scope of this section, a brief description of steps to take when conftonted with uncertainty in an economic analysis is provided. In the second context, predicting economic decisions of others, analysts must sometimes model the response of consumers and other decision makers to uncertainties in a market. For example, energy consumers make appliance decisions under uncertain fbture %el prices. The basis for many such market decisions are rudimentary (i.e., the appliance consumer does not perform an analysis accounting for uncertainty as advocated in this section). Analyses, when these consumer decisions are important, must in some way account for this less rigorous response to Uncertainty. Simulation of a response by others to uncertainty may require using approximation methods, such as riskadjusted discount rates.
Uncertainty in Economic Evaluations
Figure 21 shows an example of the single most important form for presenting uncertain information: a probability density function (PDF). The probability density function represents a mathematical description of the probability or likelihood of an uncertain variable taking on a given value? Figure 21 represents a common shape for variables that have positive values, such as prices and quantities. Very small values are unlikely. There is a maximum likelihood at some finite value and a long "tail," which represents small probabilities of very large values for the variable. The probability distribution over electricity price shown in Figure 21 will be used in an example later in this section.
25
20
T
15
10
0,04
a,o6
a ,i
Price, $/kWh
Figure 21. Probability density
'qechnically, the probability of a random variable taking on any exuct value (e.g., exactly 1.0) is zero. However, the probability of the variable lying in a small range around that value (e.g., between 0.99 and 1.01) is given by the area under the density function between those two values,
b
Probability [ a ~ x d b ]= sf(t)dt ,
a
where f(*) is the density function.
28
Several advantages of this kind of representation for uncertah variables can be seen immediately. At the simplest level, presenting information in this form acknowledges that the value in question is uncertain. This recognition reduces the temptation to rely solely on deterministic analysistreating uncertain variables as if they were known with certainty. At the sitme time, developing a density hnction for key uncertain variables lays the foundation for an analysis that makes maximum use of the information the analyst does have about uncertain variables, imperfect as it may be. In addition, variables that have been described by probability distributions can be used as inputs to formal decision analysis. Figure 22 illustrates an alternative presentation of the PDF. Here, the cumulative distribution, which corresponds to the probability density hnction shown in Figure 21, is di~p1ayed.l~ Figures 21 and 22 capture the uncertainty in a single variable. However, there will frequently be more than one uncertain variable in an economic evaluation. The (ioint) density function of r such random variables could be represented by a graph similar to Figure 21 but with r + 1 dimensions instead of 2. Often the uncertainty in one variable will be related to the uncertainty in another variable. For example, in the economic evaluation of a dual fuel combustion turbine capable of burning natural gas or oil, the price of the two fuels may be uncertain, and, some would argue, highly correlated. Economic evaluations with such a correlated or dependenti8variable must explicitly consider such correlation. Variability can also be captured by the density and cumulative distribution functions of Figures 21 and 22. The magnitude of the density function is a function of the frequency with which the variable takes on each value over the population. For example, a density function portraying regional variations in the price homeowners pay for electricity will have its peak at the most frequently occurring price. Although there are some important distinctions between variability and uncertainty that can require different treatments, the steps described below for economic evaluations under uncertainty can also be applied to economic evaluations with inputs that vary over the population (e.g., variation in the consumer price of compact fluorescent light bulbs).
17Theprobability density function and cumulative distributions contain exactly the same information. One can be derived Erom the other by means of the relationship
where F<()is the cumulative distribution and f(.) is the probability density function. In the other direction, the relationship between these two functions is simply
¡°A pair of random (uncertain) variables xl, xz are said to be independent if their joint density functions can be represented as the product of their individual (marginal) density functions as follows:
Where f(x,, x2) is the joint density function over xi and x , taken together, and f(x,) and f(x,) are the marginal densities of the variables individually. Variables that are not independent are said to be dependent. The concept of independence generalizes in a straightforward way to sets of more than two variables.
29
Probability (Price 6 T)
0'
I
.o2
I
I
I
I
I
1
06 Criterion Price, T, $IkWh
,04
.oa
I
I
I
0.1
Figure 22. Cumulative distribution
Four steps should be taken to characterize the uncertainty in the economics of a given project.
1. 2. 3. 4.
Determine the economic measures. Determine the parameters that cause the most variation in the economic measures. Assess probability for each critical parameter. Determine the probability distribution.
The first step determines which economic measure or measures will be used for the evaluation (e.g., total lifecycle cost, levelized cost of energy, internal rate of return, and so on). The second step, known as deterministic sensitivity analysis, involves varying the project parameters over judgmentally determined ranges to reveal which parameters cause the most variation in the economic measure. In addition to identifying the most sensitive inputs, sensitivity analysis also provides insights into the range of possible outcomes and their likelihood.
For example, suppose that an organization is considering an investment in an independent power project. It is estimated that the plant will sell 1,500,000 k w h annually at 4.0 cents per kwh. This will generate $60,000 in annual revenues. Annual operation and maintenance (O&M) is estimated to be $20,000. Thus, annual profit will be $40,000. The initial plant investment will be approximately $250,000 and last for 15 years. Discounting these constant dollar cash flows over a 15year life at a 6.0%real rate equates to a project NPV of $138,490. Suppose that the values used for the economic analysis are considered "most likely" and that several of the variables used for determining the NPV are uncertain. A sensitivity analysis to determine which of the uncertain variables significantly affects the results should be performed. Table 29 illustrates the process of deterministic sensitivity applied to these variables. In the table, the "most likely" values for the parameters, as illustrated in the previous example, are depicted as the base case. In the last four columns, one variable at a time is variedin the direction that will decrease NPV (indicated by highlighting). The range over which the values are varied is determined simply by expert
30
Table 29. Variables for the Example of Deterministic Sensitivity Analysis
Base
Parameters
Case (Most likely)
Quantity Varied
Price
Varied
O&M Varied
Initial Investment
Varied
judgment. Over these ranges, as illustrated, NPV is quite sensitive to price and quantity, and not very sensitive to O&M costs or project capital costs. One useful extension of this type of sensitivity analysis for an individual variable is scenario analysis. Scenario analysis better defines the range of possible outcomes by deterministically v q i n g a number of dependent variables simultaneously to allow for their correlations. For example, if the level of annual O&M w a s related to the level of annual kwh sales, it would make sense to vary both parameters simultaneously to account for this interdependency. The third step, probability assessment, is required only for those parameters to which the project economics are sensitive. In this step, each of the critical parameters is described in terms of a probability density function or its equivalent, and correlations between dependent variables must be determined. (An introduction to the practice of both deterministic sensitivity and probability encoding can be found in Howard 1977; 2990.) In our example, the deterministic sensitivity analysis indicated that the model is sensitive to price and quantity. Figure 21 gave an example density function for price in this simple model. A density function for quantity must also be generated and is illustrated in Figure 23.
The implications of these input probabilities are worked out in the fourth and final step called change of variables. This procedure uses the given probability information about the project cost and performance parameters along w i t h the deterministic model to determine the probability distribution governing the measure of the economic value of the project.
Several methods are available for accomplishing the change of variables. The most straightforward of these is the Monte Carlo procedure, in which the deterministic model is nrn a number of times, sampling from the input distributions (of all the random variables) each time to build up histograms that approximate the distributions o f the measures of economic value (Hammersley 1965). Some shortcuts, such as Latin Hypercube Sampling, can be used to reduce the number of model runs that would be
31
0.7 0.6
T
0,5
0 4 02 082 0.1
~ O O O O O ~oaooaum o o a o 2000000 2 5 0 ~ 0 0 0~ounooo
Annual Sales, kWh
Figure 23. Probabilifiy distribution aver quantity
required for Monte Carlo analysis. For economic analysis embodied in a spreadsheet, commercial addins are available to carry out both Monte Carlo and sampling procedure^.'^
The end result of these procedures will be probabilistic descriptions of the chosen economic measures applied to the project. These descriptions can be expressed in several ways, the two most common being the probability density Eunction and the cumulative distribution, illustrated in Figures 21 and 22. The density function illustrates most directly which values of the economic value measure are more likely and how the relative likelihood changes over the range of possible values. The cumulative distribution, on the other hand, can be used directly to answer questions such as, "What is the probability that the value lies in a specified range?"
Figure 24 illustrates the probability distribution over the project NPV resulting from the simple model described previously. This information was generated by a commercial software package (Crystal Ball) using Monte Carlo simulation.
This analysis illustrates the importance of the probability density representation of the project's net present value. Looking at the project economics when dl the variables are set at nominal values indicates a substantially positive NPV. However, the sensitivity analysis reveals the possibility that uncertainties in price and quantity could lead to a negative NPV. The summary in Figure 24 is the most revealing. The most likely values of NPV, as it turns out, are the negative ones. The cumulative distribution curve of Figure 24 would reveal that the odds are less than fiftyfifty of achieving a positive NPV. Even in this drastically oversimplified model, it would have been difficult to foresee this conclusion from the basic information about input variables.
I
lgCrystalBall, distributed by Decisioneering Software, Lakewood, Colorado, is one example of addin software for performing uncertainty analysis. This package is an addin for Excel and w a s used to develop the example shown in Figure 24.
32
Figure 24. Profit forecast frequency chart
Modeling Behavior of Others Under Uncertainty
As mentioned in the previous section, uncertainty can arise when trying to predict the economic decisions or actions of others (e.g., how will electricity consumers react to an increase in electricity price). The normative approach to this modeling issue would be to assume that dl parties within the population use the equivalent of decision analysis.
There are at least two major problems with this approach. First, the application of decision analysis within a market model would generally involve far too much effort to be practical. More importantly, there is considerable evidence that energy consumers often behave very differently from the strict economic rationality assumption taken in the normative model.
It is fair to say that no truly satisfactory solution to this modeling problem has emerged. Most common approaches begin with some kind of normative model and then adjust it in some way to make it better match observed data on consumer choice. For example, logit models are one way of handling the observed fact that the cheapest source does not capture 100% of the market (Packey 1993). Multinomial logits can account for decision makers' consideration of factors other than simply the economic value of an investment while capturing the uncertainties and variabilities of decision makers and investments.
Another means of representing consumer behavior that deviates from the normative model is to increase the discount rate that consumers in the model use to evaluate energy equipment purchase decisions. Two rationales are commonly used for this approach. First, higher discount rates make projections of consumer choices look more like the observed data on these choices. However, such model projections still have trouble comparing well with observed data because factors other than energy costs are critical in purchase decisions.
Second, such higher discount rates are often used as an adjustment to capture the risk inherent in an investment. The riskadjusted discount rate argument proceeds as follows. Investments in energy efficiency or renewable energy can be risky. One response to the evaluation of risky investments is the use of a discount rate higher than the one that is appropriate for riskfree investments (a riskadjusted discount rate). Thus, the risk assumed by making investments that do not produce the anticipated remns is offset by investments producing this higher adjusted rate of return.
33
There is considerable controversy in the financial community regarding the appropriateness of a riskadjusted discount rate approach. Increasing the discount rate is a poor substitute for explicitly capturing the uncertainty in input variables. Not only is the riskadjusted discount rate approach inappropriate for EE analysis, but the extent of its use in others¡¯ evaluatiqn of energy investments is not known. Thus, using it to simulate others¡¯ investment decisions is questionable.
34
3 Selection Criteria Guide
This section presents some different measures of the economic value of an investment. The choice of which measure is used to evaluate an investment is determined by several factors. These factors include the investor's perspective, regulation, risk, financing, cash flow, comparison of mutually exclusive alternatives, similarity o f alternatives' benefits, whether the investment is fully defined in terms of its size and use, and so forth. Most of the economic measures are valid for most investments, and it is usually a good idea to compute several of the measures to better evaluate the investment. However, certain measures are clearly inappropriate for some investments. The use of the internal rate of return to compare two projects with significantly different returns over time, for example, may result in inappropriate assumptions regarding the rate of return available through reinvestment of the cash inflow.
Table 31 is a quick reference for identifying the appropriate economic measure for different investment features and decision criteria. Letters in the table indicate whether the measure is recommended, generally not recommended, or commonly used. A blank cell signifies that the measure is acceptable. An "R' signifies that the measure is recommended. However, this does not mean that the other economic measures are inappropriate. On the other hand, an "N" means that the measure is generally not recommended and may yield incorrect results and conclusions. Finally, "C" denotes that the measure is commonly used to evaluate investments with the specific feature. Inasmuch as each investment and investor is different, the best measures to use cannot be categorically stated within a matrix as simple as this one. This matrix is simply a quick reference from which the reader can identify those measures he or she may want to investigate thoroughly.
To be more explicit, the entries in the matrix should be viewed as general rules for which there will be many exceptions. For example, according to the investment decisions portion of the matrix, (TLCC)and revenue requirements (RR)are not listed as "recommended' for any decisions. Yet these two measures are clearly applicable for those cases in which the energy services provided by the alternatives are identical, or in which the energy service must be secured and cost is, therefore, the only issue. These measures are not recommended in general simply because they do not consider benefits or returns.
A more detailed description of investment features and decision criteria in the matrix is in the next section. Included is a description (definition) of each of the terms identified as investment features and decisions. Also included is an explanation of each of the entries contained in the economic measure matrix; e.g., why was IRR recommended as opposed to not recommended for different investment features and decisions. In addition, each economic measure discussed includes a brief discussion of its use (whether recommended, commonly used, or not recommended) €or different investment features and decisions. The makix cannot include all possible investment feature and decision possibilities; nor can it include all possible combinations, e.g., acceptance or rejection of a mutually exclusive regulated investment.
Explanations for the Economic Evaluation Measures Matrix Investment Features
Investment after return: A significant investment (net negative cash flow in the year) is required after the investor has received some cash inflow from the project.
Explanation of Entries: IRR is not recommended because a net negative investment after a positive return can result in multiple positive IRR values, and because downstream investments are improperly discounted, i.e. at the IRR and not at the investor's discount rate. MIRR is acceptable because it avoids both of these problems w i t h IRR.
35
f Economic Measures Applying to Specific Investment Features Table 31. Overview o and Decisions"
,
investment Features
Investment after return
NPV
TLCC
RR
LCOE
IRR
N
MlRR
SPB
DPB
BK
SIR
Regulated investment
Financing Risk Social costs Taxes Combinations af investments
R
N N
N
C,R
R
c,R
N
c,R
N
1
Investment Decisions
Acc ept/r ej ect
I
NPV
I TLCCb I RRb I
N
LCOE
I
lRRb
C
I MlRR
N
SPB
1
DPB
I
WC
SIR
N
N
1
Select from mutually exclusive alternativesb Ranking (Limited budget)
R
C
N
R  Recommended N  Not recommended C  Commonly Used
A blank cell indicates that the measure is acceptable.
a. This table is intended t o serve only as a rough guideline by which an analyst can identify those measures that warrant further investigation. Exceptions to each of the entries will occur. b. Text discusses some of the exceptions.
Economic Measures
NPV  Net present value TLCC  Total lifecycle cost LCOE  Levelized cost of energy RR  Revenue requirements IRR  Internal rate of return
MlRR  Modified internal rate of return SPB  Simple payback period DPB Discounted payback period B/C  Benefittocost ratio SIR  Savingstoinvestmentratio

36
Regulated investmenr: The recovery of costs of an investment are regulated by a state or federal regulatory body.
. because tkis is normally the basis on which Explanation of Entries: Required revenues are recommended such investments are defended to the regulators.
Financing: This entry refers to the evaluation of investments requiring projectspecific debt financing (as opposed to those capitalized only through equity financing or corporate debt financing, accounted for by the discount rate, which reflects the cost of both equity and debt.)
Explanation of Entries: Payback measures may be used to get a quick sense of a project ignoring the financing. However, the explicit consideration of financing significantly complicates the analysis, eliminating the simplicity advantages of these measures. Thus, payback measures are not recornmended when financing is to be explicitly considered. The savingstoinvestment ratio is also not recommended because of the issue of whether the investment is defined as only the equity portion of the investment or the total investment.
Risk: All investments pose some risk that they will not provide the promised returns. For those investments with significant uncertainties, risks should be explicitly considered.
Explanation of Entries: Payback measures are recommended because they provide a quick assessment of the duration of the period during which the investor¡¯s capital Is at risk. More €orma1 evaluation of risk (e.g., decision analysis), as described in the manual, is also recommended. Social costs: The full cost of an alternative, including both direct costs such as capital costs and O&M costs as well as external costs such its environmental costs, k, all costs incurred by society are considered. Explanation of Entries: Net present value and benefitlcast ratios are acceptable and are commonly used for the evaluation of investments from a social perspective, and therefore, are recommended measures.
Taxes: Taxes affect the value of most investments and should therefore be considered explicitly in all but the most rudimentary analyses. Taxes to be considered include state and federal income taxes, property taxes, and so forth.
Explanation of Entries: Inclusion of taxes in payback calculations complicates the analysis, eliminating the simplicity advantages of payback measures. Therefore, payback measures are not recommended.
Combinations of invesments: Occasionally an jnvestment in one energy technology will have an impact on the cost, performance, or value of another energy investment. For example, the use of additional insulation in a building¡¯s walls will decrease the value of a more efficient furnace. In these cases, the investments should be evaluated as a combined system, i.e., as a single investment, with the cost, performance, and value reflecting the attributes of the combined system.
Explanation of Entries: All measures are acceptable subject to the other considerations, as given for the other investment features and types of decisions.
Investmeni Decisions
Acceptheject: A single investment is under consideration. It can either be accepted or rejected.
37
Explanation of Entries: TLCC and RR are not recommended because they provide no frame of reference as to what are acceptable costs and they do not consider benefits and returns. IRR is acceptable (within the constraints mentioned in the Investment Features portion of the matrix) and is commonly used for many acceptlreject decisions because it allows a quick comparison w i t h a minimum acceptable rate of return (hurdle rate) that represents the opportunity cost of capital to the investor.
Select from mutually exclusive aZ&matives: Only one set of investments can be selected. This might occur because the investments comprise different methods or designs for providing the same service or because different size systems are being considered to provide different levels of the same kind of service.
Explanation of Entries: If the retums and benefits are the same for all alternatives, then any one of the measures is acceptable. However benefits frequently vary in terms of the time of major returns, unequal lifetimes, services, or output. Because the choice of one alternative precludes taking advantage of the other alternatives, most measures are not recommended because they fail to recognize the difference in the size of the investments (e.g. LCOE, IRR, MIRR, payback, B/C, SIR); a large investment allows the investor to invest more of his or her assets at a favorable return (incremental analysis of the larger investment compared to the smaller investment can rectify this shortcoming of these measures). TLCC and RR are not listed as "recommended" because they do not explicitly consider returns and benefits. TILCC is commonly used to choose between energy efficiency investments that provide identical benefits. NPV is recommended because it explicitly determines the value by giving larger projects credit for potentially larger returns.
Ranking: Ranking of investment alternatives is used to select one or more investments from a set of nonrnutually exclusive investment alternatives. Usually the selections are constrained by budget, cash flow, or other resources. The objective of the analysis is to select the set of investments that will maximize the value to the investor from his or her available investment funds.
Explanation of EnQies: TLCC and RR are not listed as "recoinmended" because they do not explicitly consider benefits and returns. IRR is not recommended because It implicitly assumes reinvestment of returns at the IRR, and therefore, overvalues projects w i t h early returns. Unless risk is a major consideration, payback methods are not recommended because they ignore returns after payback. NPV is acceptable but requires the evaluation of each combination of different investments that meets the resource constraints. LCUE, MIRR, B/C, and SIR are recommended because they provide the proper ranking of projects, which are then selected in the order of their rank until the resource budget is exhausted?
OFor analyses in which the surn of the investment costs (i.e., resource requirements) of the high priority investments do not sum exactly to the budget (i.e., resource constraint), there is a possibility that some other combination of the low priority tasks that uses a larger portion of the budget will provide more value to the investor. For a small set of investment alternatives, the analyst can usually identify the optimum set by inspection of or by computing the NPV for all combinations; for larger numbers of alternatives, integer linear programming can be used.
2
38
4 Economic Measures
This section includes an overview of the procedures involved when developing net present value (NPV), total lifecycle cost (TLCC), levelization, unadjusted and modified internal rate of return, simple payback (SPB), discounted payback (DPB), benefitkost (B/C) ratios, savingslinvestment ratios (SIR), B/C ratios related $0integrated resource planning, and consumerlproducersurplus analyses. Evaluation software (the diskette is provided with this manual) has been developed to help analysts tackle investment problems that are traditionally difficult to evaluate manually. The evaluation software automates the exact equations for the first eleven economic measures in this section. It is hoped that this program will improve the speed and precision with which analysts apply the methods and procedures in this section.
The selection criteria guide presented in the previous section relates to this section by suggesting which economic measures are most appropriate for a specific analysis. Different economic measures apply to different situations, and it is generally a good idea to use several when evaluating an investment. The economic measures described in detail in this section can be used to compare alternative investments or projects. The methods for using these measures as comparison tools are fairly straightforward and are covered in more detail in the specific section dedicated to the measure. For example, costeffective alternatives are those with the lowest TLCC,revenue requirements (RR), LCOE, SPB, and DPB; and the highest NPV, internal rate of return (IRR), modified internal rate of return (MIRR), B/C, and SIR. However, the analyst should be aware that when comparing alternatives, different measures may not always provide the same answer. For example, simple payback requirements reject an alternative that, while having a longer payback period, has strong longterm returns. Sometimes the objective of an evaluation will be to find the most costeffective combination of separate investments. If the objective is to determine the most costeffective combination of airconditioner size and amount of insulation, then each combination should be evaluated collectively, not on a componentbycomponent basis, because separate components of the combinations affect one another. So, when considering a more efficient air conditioner and the upgrading of insulation, the most costeffective alternative is probably a combination of improvements to both the air conditioner and the insulation (Ruegg and Petersen 1987).
Net Present Value
Infroduction
The NPV of a project is one way of examining costs (cash outflows) and revenues (cash inflows) together (Palm and Qayum 1985). A NPV analysis can be composed of many different cost and revenue streams. The analyst must know the form of the different streams (current or constant dollars), so the correct discount rate can be used for the present value analysis. Alternatively, the cash flows can be adjusted to reflect the form of the discount rate.
NPV analysis is recommended when evaluating investment features and decisions such as mutually exclusive projects and social costs. With mutually exclusive projects, NPV does not fail to recognize the difference in the size of investment alternatives (i.e., a large investment allows the investor to invest more at a favorable return). For social costs, NPV is not only acceptable but is commonly used when evaluating investments from a societal perspective. It is also recommended that NPV be used in most other evaluations as well, specifically as a secondary measure to check the validity of any primary measure used.
39
Discussion
The formula for NPV can be expressed as:
NPV=C
n d
F n
(1
+
d)"
= F,
+
F, (1 + d)'
" +
(1 + d)2
F2
+
... 4
F N (1 + d)N
(41)
Where:
NPV = net present value = net cash flow in year n = analysis period = annual discount rate.
F n
N
d
I
I
1
For exampJe, assume an investment of $10,000 made at the beginning of the year, no salvage value, and O&M costs21 of $2,300 in year zero, inflating at an assumed inflation rate of 3% per year thereafter. Furthemore, assume that the investment is not replaced, a 5year doubledeclining depreciation schedule, a marginal federal income tax rate of 34%, no state income tax, and a nominal discount rate of 12%. In addition, the investment produces 1000 units of energy in the first year of operation, 950 in the second, 925 in the third, and 900 in the fourth and fifth. The energy is sold for $10 a unit in year zero, inflating at 3% per year thereafter. Table 41 illustxates the current dollar aftertax cash flow calculation.
Table 41. Calculation of Current Dollar AfterTax Cash Flow
Net Taxable
Investment Year
O&M Costs
Federal
AfterTax
Revenues (c)
$0
Depreciation
Income
(e) = (cbd)
h o m e Tax
Cash Flow
(9) = (cabf)
$ f0,000
(4
$ 10,000
0
0
0
0
(b)
$0
(d)
$0
(9 = e x tax
NA
$ 1,687
0
1
NA
$4,961 6,300
1,339
1,379
1,421
10,300
10,079
4,000
2,400
7,274
6,558
2
3
2,142
10,108
10,130
1,440
1,080 1,080
7,247
2,464
2,580
6,223
6,087
4
1,463
1,507
7,587
7,847
5
0
10,434
2,668
6,259
Aftertax cash flows are now applied to the NPV formulation (discounted at 12%) to calculate the NPV as shown in Table 42.
'lFor the purposes of this manual, O&M represent annual operating, maintenance, and %el expenses.
40
Table 42. Net Present Value of Current Dollar Cash Flows
Present Value interest Factor (PVIF)
Period
Cash Flow
$(10,000)
Present Value
$(10,000)
7,274
6,558
6,223
6,087
0.8929
6,495
0.7972
0.71 18
5,228
4,430 3,868
0.6355
6,259
0.5674
3,551
NPV = $13,572
The positive NPV of $13,572 shows that the investment is economical. The investor would have been indifferent as to whether to make the investment had the W V been zero, whereas a negative NPV would have indicated that the returns are worth less than the initial cash outflow and the investment is not a good
one.
The results of this example would have been the same if constant dollars had been used instead of current dollars. For example, assume the same parameters as those in the previous example, except this time assume constant dollar O&M costs ($1,300 per year in base year dollars) and a constant dollar sales price ($10 per unit in base year dollars). Because depreciation in each year is calculated as a percentage of the initial investment, it is necessary to convert cash flows for depreciation from current to constant dollars using the inflation rate; i.e., constant depreciation,= current depreciation, x (1  inflation rate>¡±.Table 43 illustrates the constant dollar aftertax cash flow.
Table 43. Constant Dollar AfterTax Cash Flow
O&M
Net Taxable Revenues
(c)
Federal
Af terTax
Investment Year
(a)
Costs
Depreciation
Income
(e) = (cbd)
(b)
(d)
Income Tax (f) = (e x tax)
Cash Flow
(9) = (cabf)
,
Aftertax cash flows are now applied to the NPV formulationdiscounted at 8.74%; i.e., [(l+nominal discount rate) / (1 + inflation rate)]  1 = 1.12/1.03  1 = 8.74to calculate NPV, as shown in Table 44.
41
Table 44. Net: Present Value o f Constant Dollar Cash Flows
Present Value
Interest Factor
Period
0
Cash Flow
$(10,000)
( I l l+ d)
Present Value
$(I 0,000)
1
7,061
6,180
5,694
0.91 96
6,495
2
0.8457
0.7777 0.71 52
5,228
4,430
3,868
3 4
5,407
5,397
5
0.6577
3,551
NPV = $13,572
The NPV calculation results in the same answer regardless of the dollar basis. This will always be the result if proper discount rates are applied to appropriate cash flows.
Although the positive NPV indicates that this is a good investment, the analyst must be careful because good investments are not necessarily the best ones. Refer to Section 3, Selection Criteria Guide, for guidance as to the appropriate application of economic measures to use for different investment types.
Total LifeCycle Cost
Total lifecycle cost (TLCC) analysis is used to evaluate differences in costs and the timing of costs between alternative projects. TLCCs are the costs incurred through the ownership of an asset over the asset¡¯s life span or the period of interest to the investor (Brown and Yanuck 1980). Only those costs relevant to the decision should be included in the malysis. TLCC analysis considers all significant dollar costs over the life of the project. These costs are then discounted to a base year using present value analysis. Any revenue generated fiom the resale of the investment is also discounted to the base year and subtracted from present value costs. TLCC is not recommended for economic evaluation to decide whether to accept or reject an investment because TLCC provides no frame of reference for what are acceptable and unacceptable costs, and TLCC does not address benefits and returns. TLCC can be used for ranking or selecting among mutually exclusive alternatives that provide exactly the same benefits and returns.
I .
TLCC analysis is composed of many different costs, and, as with NPV analysis, the analyst must know the form of the cash flows (current or constant dollars), so the correct discount rate can be applied. If the cash flows are not discounted using appropriate rates, the analysis will be flawed.
42
Discussion
Analyses associated with the governmental sector, nonprofit organizations, or the owneroccupant residential sector do not need to include income taxes because the government and nonprofit organizations do not pay income taxes and residential customers makeinvestments for the service those investments i t h home mortgage or home equity provide to them, not to generate taxable profits (unless financed w funding). Normally, analyses associated with one of these aforementioned groups will include lifecycle cost, whereas private industry will be more concerned with the NPV of a particular investment. The formula for calculating TLCC is as follows:
Where:
TLCC
= present value of the TLCC
cn
N d
= cost in period n: investment costs include finance charges as appropriate; expected
= analysis period
salvage value; nonfuel O&M and repair costs; replacement costs; and energy costs
= annual discount rate.
As an example, in addition to the parameters assumed in the previous NPV example, assume that the investor is a nonprofit organization with a n investment of $10,000; no salvage value; and O&M costs of $1,300 in year zero, inflating at an assumed inflation rate of 3% per year thereafter. Also assume the investment is not replaced, no income taxes, and a nominal discount rate of 12%. Table 45 illustrates this example.
Table 45. Current Dollar TLCC Evaluation Current Dollar O&M Costs
$0
Year
Investment
$ 10,000
Discounted Investment
$ 10,000
0
0 0
Discounted O&M Costs (w/ 12% nominal)
$0
0
1,339
1,379 1,421 1,463
1,196 1,100 1,011
930
0
0
0
0
0
0
1,507
855
$ 5,091
NPV
$ 10,000
I
The TLCC for the example in Table 45 is $15,091. As with NPV, this result is the same whether calculated using current or constant dollars, but the discount rate and cash flows will. be different. In year zero constant dollars, annual O&M costs are $1,300, which must be discounted at the real discount rate of 8.74%
43
Table 46. Constant Dollar TLCC Evaluation
I
Year
Investment
$ 10,000 0
I
Discounted Investment
$ 10,000
Constant Dollar O&M costs
$0
1,300
1,300
Discounted O&M Costs (w/8.74% real)
$ 0
0 0
0 0 0
I
1,196
0
0
0
1,100 1,011
1,300
1,300
1,300
930
855 $ 5,091
0
NPV
TLCC = $15,091
$ 10,000
I
Inasmuch as the costs associated with most conservation and renewable energy technologies can be classified as either investment costs or O&M costs (to include fuel), the formula for TLCC for a nonprofit organization can be expressed as
TLCC = I + PVOM (43)
Where:
I = initial investment PVOM = present value of all O&M costs, or PVOM = ENnz1 O & w ( 1 + d)".
Analyses of investments by forprofit organizations must consider taxes in TLCC calculations. Similar to the different forms of the fixed charge rate (see the Fixed Charge Rate subsection in Section 2), TLCC can be calculated in three different ways, depending on how taxes are treated, as shown in Table 47. The simplest calculation, which ignores taxes aItogether, is appropriate for residential (owneroccupant), nonprofit corporations, and government investments (shown in column 1 of Table 47). Actual costs (after tax deductions), as shown in column 2, are appropriate for all investments for which taxes are relevant, and it can be assumed that the tax deductions provided by the investment can be realized against income from the investment or other sources. Column 3 expands fiom the aftertax costs of column 2 to the beforetax revenue required to cover those costs. These required revenues are frequently used in the utility sector and are discussed in more detail in the subsection, Revenue Requirements, in Section 4. Rehxning to the previous TLCC example, suppose the f i r m is a private investor and income taxes are a relevant cost. Once again, assume the same parameters as in the NPV example with an investment of $10,000 made at the beginning of the year; no salvage value; and O&M costs of $1,300 per year (current dollars) in year zero, inflating at 3% per year thereafter. Also assume the investment is not replaced, a
44
Table 47. TLCC Variations
(1)
(2)
Cost After Tax Deductions
No Taxes
Formula
(31 BeforeTax Revenue Required
I + PVOM
Residential, nonprof its, government
I  (T x PVDEP) IPVOM(1  T )
Commercial, industrial
[I  (T x PVDEP) + PVOM(1  T)] / (1  T)
Utility sector
Application
I PVOM T PVDEP
= initial investment
= present value O&M costs = income tax rate
= present value of depreciation
5year doubledeclining depreciation schedule, a marginal federal income tax rate of 34%, no state income tax, and a nominal discount rate of 12%. To find the aftertax cost to the investor, the formula in column 2 can be used to calculate a TLCC of $10,705. This is illustrated in Table 48.
If the forprofit investor is a utility, the beforetax revenues required to cover the aftertax costs may be desired. In accordance with the formula in column 3 of Table 47, this can easily be accomplished by dividing the aftertax costs by (1  T) to yield a TLCC of $16,220.
Table 48. AfterTax TLCC Evaluation
Discounted Investment
$ 10,000
0
Year
Investment
$ 10,000
$ 0
$0
,196
,100
0
0
$ 4,000
2,400
$ 3,571
1,913 1,025
686
61 3
I
1,339
0
0 0
1,379 1,421
1,463
0
0
1,440
1,080
,011
930
0
NPV
TLCC = 10.000
0
I
1,080
1,507
855
$ 10,000
$ 7,809
$ 5,091
 (0.34 x 7.809) + (5.091 x 0.66) = $10,705
Using TLCC calculations to evaluate the costeffectiveness of energy efficiency investments requires calculating a TLCC both with and without the investment. For example, a 75watt incandescent light bulb operating 6 hours per night throughout the year will require 164.25 kWh annually to operate. At 6 cents per kWh this equates to $9.86. If it is assumed that electricity costs remain at 6 cents per kWh and a bulb needs replacing once a year at a cost of $1 per bulb, a TLCC (using a 12% nominal discount rate) is
45
calculated to be $39.56 for 5 years (assuming the bulb is purchased at the beginning of each year, and the electricity is paid for at the end of each year). An alternative would be to purchase a more efficient 40watt fluorescent bulb that will last for 5 years. Under the same usage patterns as the alternative, the 40watt bulb will require 87.6 kWh per year to operate. Assuming a $15 initial investment and the constant 6 cents per kWh for purchasing the electricity, a TLCC o€ $33.95 is calculated. Thus, the net savings, on a TLCC basis, of installing the more efficient 40watt bulb is $5.61.
Revenue Requirements Infroduction
Revenue requirements (RRs) are often calculated in regulated industries, such as the electric power markets, for a firm (utility) as a whole. The discussion here is directed toward the revenues required to cover the costs associated with a specific project, not a firm. The RR is the total revenue that must be collected from customers to compensate a firm for all expenditures (including taxes) associated with a project. It is actually no different than the beforetax revenue required of the TLCC outlined eadier, The RR economic measure is recommended as an appropriate measure when evaluating a regulated investment. The general decision rule for utilities is to choose the alternative for which the present value of the multiperiod investment revenue requirement is the lowest (assuming the services provided are identical) (Charles River Associates 1986). Businesses apply the RR method to project costs over an investment¡¯s useful life. Because RR is normally the basis on which regulated investments are defended, it is the recommended measure for evaluating such investments. RR is not recommended for economic evaluation when deciding whether to accept or reject an investment because RR provides no frame of reference for what are acceptable or unacceptable costs and benefits and returns are not addressed.
Discussion
The formulation of the revenue requirements approach w a s laid out in the Total LifeCycle Cost subsection in Section 4 as the beforetax revenues required, or
RR
= TLCC =
1  (T x PVDEP) + PVOM(1  T) (1  T )
(44)
Where:
RR TLCC I T PVDEP PVOM
= revenue requirements
=
total lifecycle cost
= initial investment
= income tax rate
= present value of depreciation expenses
= present value of operating and maintenance expenses.
As w a s calculated in an example in the Total LifeCycle Cost subsection, the beforetax required revenue calculated was $16,220. The same result is shown in Table 49 on a yearbyyear basis.
46
Investment decisions using revenue requirements are made by comparing the present value RR of alternatives that accomplish the same desired result. The alternative with the lowest RR is considered to be more economical.
Table 49, BeforeTax TLCC Evaluation
Discounted Investment
$ 10,000
0
0
Year
0
Investment
$ 10,000
0
Depreciation
Discounted Depreciation
O&M
Costs
$0
Discounted O&M Costs
$0
1
$ 4,000 2,400
1,440
$ 3,571 1,913
1,025
1,339
1,379
1,196
1,100
2
3
0 0
0
0
0
1,421
1,463
1,011
930
4
1,080 1,080
686
613
$ 7,809
5
NPV
0
0
$ 10,000
1,507
855
$ 5,091
Revenue requirements are an example of a present value that can be annualized (discussed in the Annualized Value subsection). The annualized revenue requirement can be obtained as follows:
L(RR) = PV(RR) x UCRF = PV(RR) x
d(l + d)N (1 + d)N  I (45)
Where d is either the real or nominal discount rate, depending on whether a real or nominal annualized required revenue is sought. Returning to the example with RR = $16,220,the nominal annualized required revenue, assuming the same 12% discount rate, is $4,500. These are the current dollar revenues that must be collected in each of the 5 years of the life of the investment to cover all costs, including taxes.
Levelized Cost of Energy
In froduction
The levelized cost of energy (LCOE) allows alternative technologies to be compared when different scales of operation, different investment and operating time periods, or both exist. For example, the LCOE could be used to compare the cost of energy generated by a renewable resource with that of a standard fossilfueled generating unit.
Discussion
The LCOE is that cost hat, if assigned to every unit of energy produced (or saved) by the system over the analysis period, will equal the TLCC when discounted back to the base year. LCOE is recommended for use when ranking alternatives given a limited budget simply because the measure will provide a proper ordering of the alternatives, which may then be selected until the budget is expended. LCOE is not recommended when selecting among mutually exclusive alternatives because differing investment sizes
47
are not considered (i,e,, an investor will choose to invest more in an alternative with more favorable returns). This shortcoming may be corrected by applying LCOE to the incremental costs of the alternatives. The LCOE can be calculated using the following formula:
n=l
c
N
Q, x LCOE (1 + d)¡±
N
=
TLCC, or
(46)
LC0E2¡¯ = ¡®FECC + { c [Qn i (1 + d)¡±]}
nsl
Where: levelized cost of energy total lifecycle cost energy output or saved in year n discount rate analysis period.
Thus, the treatment of taxes in the TLCC calculation will carry over to the LCOE. For example, the LCOE can be calculated for the sarne example as was provided in the Total LifeCycle Cost subsection for the private investor seeking his or her aftertax cost. In addition to the assumptions made in fie TLCC example, assume the investment produces 1000 units of energy in the first year of operation, 950 in the second, 925 in the third, and 900 in the fourth and fifth. Recall fiom the previous example that the TLCC was calculated, after tax deductions, as $10,705. The remaining task is to calculate the discounted value of the annual energy output or energy saved; i.e., CNn=,[Qn f (1 + d)¡±]. Applying this formula to the example using a nominal discount rate of 12%,the discounted value of energy output is 3391 units. Thus, LCOE = $10,705 / 3,391 = $3.16 in current dollars.
Once the TLCC is calculated, the LCOE can be figured in either current or constant dollars, regardless of the discount rates used to derive the TLCC. The form of the LCOE will be determined by the form of the discount rate used in the denominator of the equation CNnJQn f (1 + d)¡±]. In the previous example, a nomind discount rate was used in the denominator; thus, the resulting LCOE values are current values. For the same example, the LCOE based on a 8.74% real discount rate is $2.91 in constant dollars.
It is important to note that if the system output (Q) or savings remains constant over time, the equation for LCOE can be reduced as follows:
LCOE = (TLCC/Q) (UCRF)
(47)
Where:
TLCC
= annual energy output or saved UCRF = the uniform capital recovery factor, which is equal to
= total lifecycle cost
Q
d(1 + d)N (1 Id)N  1
¡°Even though it may appear in this formula that quantities are being discounted, this is actually a direct result of the algebra carried through Exom the previous formula in which revenues were discounted.
48
Using the data from the previous example but this time assuming an annual output of 1000 units per year and a nominal discount rate of 12%, the LCOE is equal to (TeCC/Q) (UCRF). The UCRF for thk example is
[o.n(i + 0.12)~] [(I + 0.12)~ 1 1 = 0.277 .
Thus, the LCOE is equal to $10,705 / 1,000 x 0.277 = $2.97.
(48)
Although $2.97 is the levelized aftertax cost, the beforetax revenues required to cover all costs is
$16,220 / 1,000 x 0.277 = $4.50 SO $2.97 / (1  0.34) = $4.503
.
(49)
This means that if the energy units are sold for $4.50 per unit in current dollars over the next 5 years and the company sells 1000 energy units per year of operation, the investor wiIl be able to pay the applicable income tax, earn 12% after taxes, and recoup the initial investment and annual O&M costs.
Suppose that a constant dollar LCOE was required for this example. The only difference required is to calculate the UCRF using a real discount rate, which in this case is 8.74% (carrying forward the previous assumption of a 12% nominal discount rate with 3% inflation). The UCRF then becomes
[0.0874(1 + 0.0X74)s] / [(l + 0.0874)5  1 1 = 0.255 .
(4 10)
Thus, the LCOE is equal to $16,220 / 1,000 x 0.255 = $4.14.
This constant dollar example illustrates a shortcut LCOE calculation. The shortcut methodology for estimating the beforetaxrevenuesrequiredLCOE requires the assumptions that the project not only have constant output, but also constant. O&M and no financing. If these assumptions can be made, the shortcut can be used with the application of the following formula:
LCOE = I xFCR +  O&M
Q
Q
(4 11)
Where: LCOE = levelized cost of energy I = initial investment FCR = fixed charge rate, in this case the beforetax revenues required FCR (see Section 2, Fixed Charge Rate subsection) Q = annual output O&M = annual O&M and fuel costs for the plant. Continuing with the beforetaxrevenuesrequired example with constant output and an FCR of 0.284, which can be calculated from the formula provided in the Fixed Charge Rate subsection in Section 2, the quick estimate of beforetaxrevenuesrequired LCOE can be calculated as:
LCOE = (10,000 x 0.284) / 1,000 + (1,300 / 1,000) = $4.14 ,
(412)
which is the same as the LCOE calculated from the TLCC.
If the investment is an energy efficiency investment, LCOE only makes sense in the context of the energy saved, Although TLCCs can be calculated for each energyconsuming system, LCOE should not be
49
calculated for an individual energyconsuming but rather for the incremental cost and savings attributable to the energyefficient system. This can be accomplished by levelizing the difference in the nonfuel (electricity) lifecycle costs of the two systems. For example, consider the energy efficiency example provided in the Total LifeCycle Cost subsection of Section 4: Alternative A: a 75watt incandescent light bulb operating 6 hours per night for a total energy requirement of 164.25 kWh per year, an unchanging 6 cents per kWh price of electricity, bulb replacement once a year at a cost of $1 per bulb. me nonfuel costs of this system are $4.03 (1 + M.12 + 1/[1.1212+ I/[l.l2l3 + l/[I.l2l4), or the discounted cost of purchasing a new bulb at the beginning of each year. Alternative B: a 40watt fluorescent bulb that lasts for the entire 5 years operating under similar conditions for a total energy requirement of 87.6 kWh per year, a $15 initial investment, and a constant price of electricity of 6 cents per kWh. The noslfuel cost of this option is just the $15 cost of the fluorescent bulb at the beginning of the analysis period.
With a UCRF of 0.277, the "nominal levelized cost of energy saved" for this example is ([154.03]/76.65) x 0.277 = 0.04 $/kWh. This 4 cents per kWh can then be comparedz3 to the nominal levelized cost of electricity, or 6 cents24per k W h in this example, to determine whether the energy efficiency investment is economical. In ehis example, the cost per unit required to save energy ($O.O4/kWh) is cheaper than it is to purchase the energy ($0.06/kWh), and thus the more efficient bulb should be purchased. Alternatively, were the cost of electricity to drop below 4 cents per kWh, the most costeffective investment would change to alternative A.
To gain a better understanding of the concept of nominal and real LCOE, examine Figure 4 1. It depicts the cost over the life of an investment and the resulting LCOE in both nominal and real terms. The cash flow lines show how nominal and real costs are equal in the base year, whereas in the future, real costs (i.e., inflationadjusted) are lower than nominal costs. Likewise, the LCOE is lower in real terms than in nominal. "he choice of real or nominal LCOE depends on the purpose of the analysis. Most shortterm studies are shown in current dollars, whereas longterm studies are frequently computed in real dollars to adjust for many years of inflation. A currentdollar analysis will more closely resemble future cash flows (especially when the investment is largely financed), and a constantdollar analysis paints a clearer picture of actual cost trends. Regardless of the method chosen, the most economical option will not change as long as all options are evaluated using the same method.
22Thereis no reasonable value to use for "Q," the annual output in the LCOE equation. To use the energy consumed by the system would be to penalize (increase the LCOE) for less energy consumption. 23Careshould be taken to ensure that taxes are treated equally for each investment. For this light bulb case, taxes are assumed not to be relevant because the investor is a homeowner. If the investor were a profitmaking firm, the full cost of electricity (6 cents in the example) should be compared with the i r m ($0.06[1  TI) should be beforetax LCOE; or, alternatively, the aftertax cost of electricity to the f compared with the LCOE aftertax deductions. 24Since,in this example, the cost of electricity as expressed in nominal dollars does not change, it is the same as the nominal levelized cost of electricity.
50
$/Unit
I
Cash Flow  Nominal
I Year
Figure 4 4 . LeveIized cost of energy cash flows
Annualized Value lntroduction
The annualizing process transforms a swing of cash flows (FJ into equivalent m u d streams. Cash flows are discounted to their net present value and then annualized by multiplying the present value of the cash flow by the uniform capital recovery factor (UCRF); i.e., [d(l + dy] i [(1 + d)"  I]. This is similar to the annualization of required revenues mentioned at the end of the Revenue Requirements subsection and can be done w i t h a single equation that combines the NPV and capital recovery factor calculations.
NPV = F, / (1 + d)"
AV = UCRF x NPV = UCRF x ENn=l Fn/ (1 + d)"
(413)
Where:
NPV AV
Fn
= net present value
UCRF = uniform capital recovery factor d = discount rate.
= annualizedvalue = cash flow in period n
Discussion
This formula can be simplified if the cash flow Fnis escalating at a constant rate A€? NPV
=
zNn=l [F,,(l + M y ] / (1 + d)"
k"
(4 14)
= Fo
= Fo[k(l  k") / (I  k ) ]
51
AV AV
=UCRFxNPV = U C W x F&k(l  kn)/ (1  k ) ]
Where:
F O
k
= cash flow to be annualized = [(l 0 ) i (1 d)].
+
+
Note that if there is no escalation in price (i.e., hp = 0), then AV = Fo. Also note that the formula for annualized cost assumes that the price escalation is measured in the same type of dollars (either constant or current) as is used for the discount rate, d.
Internal Rate of Return
Introduction
The internal rate of return (IRR) for an investment that has a series of future cash flows (IF,, F,, ... F,) is the rate that sets the NPV of the cash flows equal to zero. The IRR analysis allows for the comparison of a wide variety of investment activities. However, IRR is not recommended when evduathg investments in which further investment after return is required because downstream investments are improperly discounted and multiple positive PRR values can occur. IRR is commonly used for acceptheject decisions, allowing a quick comparison with a minimum acceptable rate of return (hurdle rate). IRR is not recommended when selecting among mutually exclusive alternatives because the values of differing investment sizes are not considered (an investor will choose to invest more in an alternative with more favorable returns). This shortcoming may be corrected by applying IRR on an incremental basis. IRR is also not recommended when ranking projects because IRR implicitly assumes reinvestment of returns at the IRR. The viability of a project is usualIly assessed with IRR by comparing the IRR of the project with a "hurdle rate" that represents the IRR of the next best alternative (the opportunity cost of capital). IRR also has the advantage that it can be used to directly compare the aftertax return on readily available financial instruments, such as bonds, thereby providing the investor with a quick qualitative assessment of the project.
Discussion
IRR equals the rate for which:
0 = NPV = EN,=, [F, 4 (1 + d)n] Where: NPV Fn d
= net present value of the capital investment
(415)
= cash flows received at time n
= rate that equates the present value of positive and negative cash flows when used as a
discount rate.
Table 410 illustrates the aftertax cash flows resulting from the use of the same example as w a s used in the Net Present Value subsection. This example involved the following assumptions: an investment of $10,000 made at the beginning of the year; no salvage value; O&M costs of $1,300 in year zero, inflating
52
at an assumed inflation rate of 3% per year thereafter; the investment is not replaced; 5year doubledeclining depreciation schedule; a marginal federal income tax rate of 34%; no state income tax; production of 1000 units of energy in the first year of operation, 950 in the second, 925 in the third, and 900 in the fourth and fifth; and energy sold for $10 a unit in year zero, inflating at 3% per year thereafter.
Table 410. AfterTax IRR
Net Taxable Income
(0)
Year
investment
O&M Costs
Revenues
(c)
Depreciation
(d)
Federal Income Tax
AfterTax Cash Flow
(9) = (cab9
(4
0 $ 10,000
(b) $0
1,339 1,379 1,421
= (ebd)
(9 = e x tax
1
2
0
0
0
0
10,30Q 10,079 10,108
4,000
2,400
$ I 4,961
6,300
$ 1,687
2,142 2,464
7,274
6,558
3 4 5
1,440
1,080
7,247
6,223
1,463
1,507
10,130
10,494
7,587
7,847
2,580
2,668
6,087
6,259
0
1,080
An IRR equal to 61% is calculated when the formula is applied to the aftertax cash flow scenario (successive approximation methods can be used to find the rate that equates the present value of cash flows to zero). In other words, the present value of this aftertax cash flow scenario is zero if a discount rate of 61% is assumed. In this scenario, if the investor¡¯s hurdle rate is higher than 61%, then the investor will more than likely invest his or her money elsewhere; whereas, if the hurdle rate is lower than 61%, the investor may view the investment as a good opportunity. It is also important to note that the 6 1%IRR is actually the nominal IRR and should be stated as such. This is the case because the cash flows on which the IRR w a s calculated were in current dollars. If the dollars had been constant, the IRR would have been a real IRR.
The equation for IRR is a polynomial of degree N and, as such, the analyst must be aware that there are N different roots, or solutions, to the equation. However, when the investment pattern is normal (i.e., the initial investment or cash outflow is followed by a stream of cash inflows), all solutions are either negative or imaginary, except for one positive solution, On the other hand, if the cash flow is such that large outflows occur during or near the end of the life of the investment, then the possibility of multiple positive roots arises (Palm and Qayum 1985). Because of the complexity of the required calculations and multiple potential roots, some software for personal computers requires a guess at the IRR prior to calculation (Lotus 2991). For situations in which there is a close approximate value, this poses little difficulty to the analyst. However, when the analyst does not have an approximate value, this could pose a problem and add doubt to the results.
IRR analysis may not fully consider the pattern of investments and returns over time. For example, two investment projects with an IRR of 17% might be considered equal, but if there are different analysis periods for the two projects (e.g., 20 years for project A and 3 years for project B), a decision maker might not be indifferent regarding the choice of A or B. That is, an investor may find a sustained 20year revenue stream at 17% more desirable than a 3year payment flow at the same rate.
53
Another shortcoming of IRR is that it may overstate profitability. An implicit assumption contained in an IRR calculation is that all1 interim proceeds from the investment are reinvested at a rate equal to the IRR. A previous IRR example provided an HRR of 61%; however, it may be unrealistic to believe that the interim cash flows will be reinvested at a rate equal to 61%. Another caution for the analyst is to be aware that when using IRR as the sole measure to compare alternative projects, the less profitable dternative may be chosen. For example, two projects with a life of 3 years and an initial investment of $10,000 are compared. The cash flows for the two projects are different, as illustrated in Table 411. A nominal discount rate of 12% is used to calculate NPVs for this example.
As illustrated in Table 411, if IRR was the sole measure used to decide on alternatives, Project B would be chosen over Project A when, in fact, Project A is the more profitable alternative using the discount rate of 12% for the NPV analysis. Worth noting is the fact that Project B might be perceived as less risky since the returns occur sooner than those of F¡¯roject A.
Table 41 I. Results of Using IRR as a Sole Measure
Year
0
1
2
Project A
$ 10,000 3,000
Project B
$ 10,000
9,000
4,000
2,000
5,000
10,000
3
IRR
28.9%
$ 3,782
3 1 8%
$ 2,648
NPV
Given these potential problems with IRR, it is recommended that IRR be used only when performing an acceptkeject analysis for single projects. The IRR is acceptable in this instance because when IRR is greater than the hurdle rate, the actual yield when accounting for reinvestment at the hurdle rate will also be greater than the hurdle rate (Ruegg and Marshall 1990).
Modified Internal Rate of Return
lntroduction
For projects of different scale and lives, it is possible for different ranking criteria, such as NPV and I E U X , to produce conflicting results because of differing reinvestment assumptions. The NPV method assumes reinvestment at the discount rate, whereas the IRR method assumes reinvestment at the IRR rate. The modified internal rate of return (MIRR) accounts for varying reinvestment rates and should be used in these circumstances. MIRR is calculated by assuming that all cash inflows received before the end of the analysis period are reinvested at the discount rate until the end of the analysis period. The terminal (future value) mount at the end of the analysis is then discounted back to the base year. The discount rate that will equate the present value (in the base year) of the terminal amount to the present value of all investment costs is the MIRR.
54
MIRR is not recommended when selecting among mutually exclusive alternatives because the values of differing investment sizes are not considered (i.e., an investor will choose to invest more in an alternative with more favorable returns). This shortcoming may be corrected by applying MIRR on an incremental basis. Because MIRR will provide the proper ranking of projects to be selected to maximize total return given a limited budget, Ml[RJ3 is recommended when ranking alternatives.
Discussion
The formulaz5for calculating an MIRR is as follows: MIRR = solution for r in the following equation:
MIRR = r, where
n=o
N c
Erin
(1 +
(I)"
= N
c
Fp,(l + d)Nn
n=o
(1
(4 16)
I 
r)N
Where:
MIRR
= r, modified internal rate of return
Fn, FPll
d
= net negative cash flows at time n
= net positive cash flows at = rate of return of reinvestment
me n
N
= life of investment.
Recall that the IRR of the aftertax cash flows in the example fkom the Internal Rate of Return subsection was 61%. Remember that IRR assumes that dl interim cash flows are reinvested at the IRRin this case 61%. As an example of MIRR, assume that dl interim cash flows are instead reinvested at 12%. Table 412 illustrates the application of MIRR versus IRR.
Table 412. MlRR versus IRR Year AfterTax Cash Flows Future Value in Year 5 Cash Flow for MlRR
2
3
4
6,558 6,223
6,087
9,214
7,806
8,817
5
IRR
6,259
61.2%
6,259
41,542
I MIRR
32.9%
251n the formula provided here the present value of negative cash flows and the future value of positive cash flows are calculated using the minimum rate of return. In some cases, different rates are used when performing these calculations.
55
As illuswated in Table 412, the future value of the aftertax positive cash flows is $41,542. The discount rate, which equates this to the original $10,000 investment over the 5year period, is 33%. Again, given the example, the MIRR should actually be labeled as a nominal MIRR of 33% because the aftertax cash flows were in current dollars, If the dollars were constant, the interim cash flows would be reinvested at the real rate of 8.74%, and the resulting MIRR of 29.2% would be a real rate.
As stated earlier, MIRR can be used to evaluate projects having different scales or lives. As an example, assume two alternative projects, X and Y, each costing $15,000, which will be invested at the beginning of year one. Project X returns $7,000 at the end of years one, two, and three; and Project Y returns $3,000 at the end of years one through ten. Assume a discount rate of 10%. In this example, the NPVs of each cash flow stream is $2,408 for Project X and $3,434 for Project Y. On the other hand, the IRR is 18.9% for Project X and 15.1% for Project Y. Thus, Project Y is the best alternative when using an NFV analysis and Project X is the best alternative when using IRR analysis. This result ignores the fact that cash inflows fkom Project X can be reinvested over the remaining 7 years of the analysis period. Given the different project lives, the analyst should calculate an MIRR. This can be done by assuming a reinvestment rate of 10% for Project X.
The first step is to calculate terminal values for Project X under alternative reinvestment rates. For Project X, the future value of the $7,000 annuity for 3 years is calculated. This is then reinvested at the discount rate of 10% for the remaining 7 years of the analysis to arrive at a terminal value (future value) of $45,152. In the case of Project Y, the future value of the $3,000 annuity for 10 years is calculated to arrive at a terminal value of $47,813. Next, calculate the discount rate, which will equate the terminal values, when discounted back to the base year, with the investment.
Project X: $45,152/(1 MIRR = 11.7%
+ d)N $15,000 = 0
(417)
(4 18)
Project Y: $47,813/(1 + d)N $15,000 = 0 MIRR = 12.3%.
The MIRR in this example reveals that given a reinvestment rate of 10% for Project X, Project Y should be undertaken, not Project X. This result matches the results of the previous example of NPV analysis. Sometimes a project will require investment near the middle or end of an analysis period after positive cash inflow has occurred, or there may simply be negative cash flows near the middle and end of the analysis period. This situation can lead to multiple positive solutions for ordinary IRR calculations. MIRR should be used in these situations.
Simple Payback Period
In troduciion
Simple payback (SPB) is a quick, simple way to compare alternative projects. It is relatively easy to utilize and as such is a very popular financial tool. Simple payback is the number of years necessary to recover the project cost of an investment under consideration. SPB is commonly used and recommended when risk is an issue (i.e., significant uncertainties are present) because SPB allows for a quick assessment of the duration during which an investor¡¯s capital is at risk. SPB is not recommended when evaluating alternatives involving financing and tax features because their
56
inclusion complicates the analysis and looses the advantages of simplicity. SPB is also not recommended for selecting among mutually exclusive alternatives because the values of differing investment sizes are not considered; i.e., an investor will choose to invest more in an alternative having more favorable returns. This shortcoming may be corrected by applying SPB on an incremental basis. When ranking projects, SPB is not recommended because it ignores returns after payback.
The SPB can be expressed as the first point in time at which:
En AI, 5 En AS,,
Where:
SPB
(419)
= minimum number of years required for the nondiscounted sum of annual cash flows net
annual costs to equal or exceed the nondiscounted investment costs
AI
AS
= nondiscounted sum value of the annual cash flows net annual costs.
= nondiscounted incremental investment costs (including incremental finance charges)
Discussion
One drawback to the SPB method is that it ignores the time value of money. That is, the use of SPB implies that there are no opportunity costs to the investor (Le., the investor¡¯s discount rate is zero) (Ruegg 1987). However, the simple payback method is easy to understand and calculate, and can be useful if there are uncertainties, such as uncertain tenure or life of the technology. When there is a high degree of uncertainty associated with future cash flows, SPB gives an indication of how long one¡¯s assumptions must hold to ensure that at least the principal is returned to the investor.
Discounted Payback Period
Introduction
The discounted payback period (DPP) is the number of years necessary to recover the project cost of an investment while accounting for the time value of money.
DPB is recommended when risk is an issue (i.e., significant uncertainties are present) because DPB allows for a quick assessment of the duration during which an investor¡¯s capital is at risk. DPB is not recommended when evaluating alternatives involving financing and tax features because their inclusion complicates the analysis and looses the advantages of simplicity. DPB is also not recommended when selecting among mutually exclusive alternatives because differing investment sizes are not considered (i .e., an investor will choose to invest more in an alternative w i t h more favorable returns). This shortcoming may be corrected by applying DPB on an incremental basis. When ranking projects, DPB is not recommended because it ignores returns after payback.
57
Discussion
DPB can be expressed as that time in which:
Where: DPB
A1 AS
d
= minimum number of years required for the discounted sum of annual net savings to
equal the discounted incremental investment costs = incremental investment costs = annual savings net of future annual costs (i.e,, AS equals the incremental energy costs, incremental nonfuel operation, maintenance, and repair costs, incremental repair and replacement costs, minus the incremental salvage costs) = annual nominal discount rate (Ruegg 1987).
As an example of the difference between SPB and DPB, assume the following:
Incremental Investment Cost Differential Annual Net Savings Discount Rate Payback Period
SPB $18,000 $3,000

DPB $18,000 $3,000 6.88% 8 years
6 years
A disregard for the time value of money is not a limitation of discounted payback (Brown and Yanuck 1980). The DPB differs fiom the SPB in that the DPB analysis uses the present values of the changes in investments and savings. Thus, when accounting for the time value of money, the payback period is longer, as illustrated above. As in any present value analysis, the cash flows or net savings in DPB can occur at times other than the end of the year. Alternative assumptions such as midyear, midmonth, or beginningofthemonth cash flows will affect the results of the analysis. See Appendix E and Koomey (1990) for further clarification.
BenefittoCost Ratios
lntroduction
Benefittocost (BIC) analysis is conducted and B/C ratios are derived to ascertain whether and to what degree the benefits of a particular project exceed the costs. Such analyses are more frequently performed for projects that involve the public interest. They range ftom direct government investments in public works (such as infrastructure, parks, or public power projects) to private investments by utilities in which the impacts on the ratepayers, investors, and the environment all may have to be considered to determine if the action is appropriate. Because B/C ratios are commonly used when evaluating investments from a societal perspective, they are recommended for use when evaluating projects in which social costs prevail. BIC ratios are not recommended when selecting among mutually exclusive alternatives because the values of differing investment sizes are not considered; i.e., an investor will choose to invest more in an alternative with more favorable returns. This shortcoming may be corrected by applying B/C ratios to the incremental 58
benefits/costs of the alternatives. BIC ratios can also be used when ranking projects if benefits predominate, particularly from a public policy perspective.
Discussion
The B/C ratio is the ratio of discounted benefits to discounted costs at a given point in time (base year). The denominator of the B/C ratio includes dl costs. Operations, maintenance, fuel, finance costs, and property taxes should be included. The numerator of the B/C ratio includes all savings, revenues, and other benefits. Externalities can be positive (benefit) or negative (cost). Some impacts of a program action, such as local economic development and environmental impacts, may be difficult to quantifj. To the extent that the externality can be quantified, the externality value should be included when appropriate (i.e., a positive externality added to the benefits and a negative externality included in costs). Quantifying externalities is covered in more detail in the Special Considerations subsection in Section 5. The h a n ) 1. determining factor in B/C analysis is whether the B/C ratio is equal to (or greater t The mathematical formula for B/C ratios is: B/C = [PV (All Benefits)] + [PV (All Costs)] Where:
PV (All Benefits) = present value of all positive cash flow equivalents PV (All Costs) = present value of all negative cash flow equivalents.
(421)
An example for the calculation of the B/C ratio follows. The calculation includes three steps: (1) the PV calculation of the cost stream, (2) the PV calculation of the benefit stream, and (3) the calculation of the ratio.
Step 1  Present value of a stream of costs
Discount rate 8.00% Cash flow per year $3,000 Time periods 3 Time period Amount
1 $3,000.00 2 $3,000.00
3 $3,000.00
Present value of an an~ual $3,000 payment for 3 years = $7,731.29 Step 2  Present value of a stream of benefits Discount rate Cash flow Time period
8.00% Varies over time
4
59
Time period Amount
1 $1,000.00
2 $2,000.00
3 $3,000.00
4 $4,000.00
Present value of 4 years of irregular revenues = $7,962.22
Step 3  Calculation of the B/C ratio
PV of benefits PV of costs B/C ratio
$7,962.22
$7,73 1.29
1.029869
The B/C ratio of the investment alternative in this example is 1.03. The higher the ratio, the greater the average dolls benefit per dollar of cost. Like analyses using IRR, B/Cratio analyses may provide results inconsistent with those of NPV analyses. As with IRR, B/C ratio analysis is acceptable for acceptlreject decisions of single projects. However, if the B/C ratio is calculated using incremental benefits and costs, it can be used to design and size projects. For example, consider the project size alternatives in Table 413.
Table 413. Projed Size Alternatives Total Benefits ($PV)
$0
15,000 18,000 19,000
Size Alternative
0
A
Totaf Cost ($PV)
$0
10,000
12,000
NPV
$0
5,000
6,000
B
C
14,000
5,000
To apply the B/C test for comparing the alternatives in this example, the alternatives would be arranged in order of increasing costs, as displayed in Table 413. Next, the B/C ratio for incremental benefits and costs is calculated. The incremental costs of Alternative A over the costs of doing nothing is $10,000, and the incremental benefits are $15,000. Thus the incremental B/C ratio is 1.5. Alternative A is now the baseline, and the incremental B/C ratio of Alternative B over Alternative A is calculated as 1.5 (3,000 / 2,000). Because the incremental B/C ratio of Alternative B is greater than 1, it now becomes the new baseline. The incremental B/C ratio of Alternative C to the new baseline is calculated as 0.5 (1,000 / 2,000). Alternative C does not become the new baseline because the incremental B/C ratio is less than 1. In this example, the most costeffective project size is Alternative B, based on the incremental B/C. The NPV values are displayed in Table 413 simply to show that Alternative B is in fact the most profitable project (Ruegg and Marshall 1990).
60
Savingsto4nvestment Ratios
Introduction
A variation of the B/C ratio, known as the savingstoinvestment ratio (SIR), is used when benefits occur primarily as cost reductions (Au and Au 1983). Although SIR is basically a B/C ratio, there is a computational difference. B/C ratios are typically calculated with dl benefits in the numerator and all costs in the denominator. In the calculation of SIR, only the principle investment costs are included in the denominator. All other costs are subtracted from the benefits in the numerator. This, in essence, makes the numerator a measure of net savings.
Discussion
The SIR ratio is recommended in ranking analyses if costs predominate, simply because SIR can properly rank projects to be selected until the budget is exhausted. SIR is not recommended for use when projectspecific debt financing is present because of the issue of whether the investment is defined as only the equity portion of the investment or the total investment. SIR is also not recommended when selecting among mutually exclusive alternatives because differing investment sizes are not considered (i.e., an investor will choose to invest more in an alternative with more favorable returns). This shortcomhg may be corrected by applying SIR on an incremental basis.
The formula for the calculation of the SIR is as follows: SIR = PV (NS) f PV (IRS)
(422)
Where:
SIR PV(NS) PV(1RS)
= savings investment ratio = present value of net savings of the activity (i.e., total savings minus all
incremental operation and repair costs not directly attributed to incremental investment costs) = present value of the sum of incremental investment costs plus incremental replacement costs minus incremental salvage vdues.
The higher the SIR ratio, the greater the average savings per dollar expended. For example, an SIR of 2 can be interpreted to mean that the investment will save $2 on average for every $1 invested, over and above the required rate of return reflected in the discount rate.
The constraints for B/Cratios outlined earlier also apply to the SIR. The SIR can be used in acceptheject decisions for single projects. SIRS should not and cannot be used reliably to find optimal sizes or designs of investment alternatives unless the analysis is based upon incremental rather than total savings and costs. An SIR computed using total savings and costs tends to reach its maximum value before the most optimal design or size is reached (Ruegg 1987). The most costeffective value is reached once the incremental savings equal the incremental costs (i.e., the incremental SIR declines to a value of unity).
63
Integrated Resource PlanninglDemandSideManagement Ratio Tests
In troducfion
Integrated resource planning (IRP) is a resource plamingpocess that considers the entire utility chain, from how customers consume electric power (demandside management [DSM]), to the alternatives available for adding generation capacities (supplyside options), As of June 1993, utilities in at least 46 states either had functioning IRP strategies or were considering, developing, or implementing an IRB process? The IRP concept is broader than traditional resource planning in several ways (Logan, Neil, and Taylor 1994):
IRP considers different analysis perspectives, evaluating the overall consequences of a program fiom
the viewpoint of the utility company, the participating consumer, the nonparticipating consumer, and society as a whole.
Public involvement methods and environmental concerns are considered in the development of the plan.
DSM options consider the fidl potential of costeffective conservation, marketing, and load management programs.
Supplyside options include both traditional and alternative generating sources.
IRP carefully analyzes the uncertainties and risks posed by different DSM and supplyside options and by external factors (Goldman, €€irst,and Krause 1989).
Including renewable energy resources in IRP requires that utility planners properly consider the relevant attributes of different renewable energy resources. Table 4 14 lists the resource attributes usually considered in the IRP process. Key attributes for renewable resources are identified with a superscript "a." The Western Area Power Administration (WAPA) has developed the Resource Planning Guide (WAPA 1993) to assist its customers in the development of IRP. The guide addresses each phase of the IRP process. The quality of a particular I W process depends on how well the following phases are linked, as well as on the quality of the data and analysis used within each phase:
Situation Analysis:
The situation analysis phase identifies problems, needs, and opportunities related to a specific utility profile. The utility profile is based on such indicators as customer mix, historical loads, projected growth, and wholesale rates. The information collected in this phase results in a list of DSM and supplyside options based on the utility's profile and a list of relevant resource attributes for each resource option.
Utilities have for years undertaken forms of leastcost and resource planning to some degree in their operations but not to the extent and without the specific regulatory context that is now prevalent.
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Screening Analysis:
The screening analysis phase helps determine which DSM and supplyside options to consider in the IRP plan. DSM screening analysis indicates whether a program is "good" and for whom it is good. The end results of DSM screening analyses are B/C ratios for each DSM option. The end results of supplyside screening analyses are levelized costs for each option.
Plan Integration:
The plan integration phase incorporates DSM alternatives into the IRP process. There are three basic integration methods ( W M A 1993): (1) static analysis, (2) the integration method, and (3) the load forecast adjustment method. Any of these methods can be used; however, the utility should choose the one that best applies to its particular situation. The following four areas must be concentrated on during this phase:
1. Determining the mix, size, and timing of resources to select the leastcost plan. 2. Deriving the resource plan according to severd conflicting objective functions. 3. Ensuring that the plan will provide equal reliability whether DSM or supplyside options are included. 4. Incorporating the hourly effects of DSM programs, program costs, revenue impacts, and market penetration rates.
Financial Analysis:
In the financial analysis phase, the utility determines how the IRP will affect its financial situation by examining: (1) revenue versus expenses, (2) cash flow and financing requirements, (3) financial ratios (such as the operating ratio), and (4) customer rate increase constraints.
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Risk Analysis:
The assumptions made during the IRP process must be made for variables that contain uncertainty. In this risk analysis phase, risks are assessed by monitoring changes in output variables as input variable assumptions are changed. Risk analysis can be performed by assigning probabilities or using sensitivity analysis, as outlined in Section 2.
Implementation:
The implementation phase is the find phase in the IRP process and varies among utility companies. Generally, the analyst presents conclusions and recommendations to the utility director, board, or council. The utility then submits the 1RP to its regulatory body. Once the IRP is adopted (usually not in its original form), the necessary implementation steps are performed.
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Table 414. Resource Attributes
Att ribUtes
Capabilitye Peak capability Energy capability Seassnalhourly profile Availability" Intemittence Forced outages Maintenance requirements Efficiency Heat rate Dispatchability Fully dispatchable Curtailable Baseloaded Location" Delivery point Modularity" Incremental size Construction/Preconsttuctionlead time
Renewable Energy Technologies
Hydro, solar, and, wind options typically have pronounced seasonal profiles. Solar and wind options also have pronounced hourly profiles. Hydro capability is dependent on hydrological conditions. Plants on the same river system are tightly correlated. Wind and solar are intemittent. Efficiency is generally not an issue for renewables because they typically rely on zero or lowcost energy sources. Runofriver hydro is nondispatchable. Pondage hydro is dispatchable. Wind is nondispatchable. Soiar thermal is dispatchable. Other solar options are nondispatchable. Biomass, landfill methane, and municipal solid waste (MSW) options are @picallynondispatchable. Geothermal is typicaIty nondispatchable. Connected at transmission or distribution level. Can be targeted to defer transmission or distribution upgrades. Incremental sizes and lead times of renewable energy technologies, except for MSW, are typically smaller and shorter than for conventional options. Lead times for MSW are 3 to 4 years. Typically no fuel costs, except biomass. These technologies provide diversification of the fuel supply portfolio.
costs Construction O&M Fuel Decomissioning costs
Incentives Tax creditsb Shareholder incentivesb Emission allowance incentives RiskDiversity" Startup delay Construction cost overrun Fuel costs O&M costs Reliability problems Premature retirement Diversity External Costs" Air and water emissions Land use Waste disposal Public safety
The 1992 National Energy Policy Act provides a 1.5 centdkWh tax credit for renewable energy producers. The 1990 Clean Air Act Amendments provide bonus emission credits for renewable energy production.
Less mature technologies may have greater construction and operating risks than conventional technologies. Renewable resources generally enhance diversity, except for hydro additions to a predominantly hydro system.
Land use and fish habitats are significant issues for hydro generation. Noise and visual impacts are issues for wind energy resources.
a. Key attributes for renewable resources. b. Applicable only to investorowned utilities. c. External costs are defined to exclude impacts that are accounted for in other cost categories, Source: D. Logan, C. Neil, A. Taylor. (1994) ModelingRenewable Energy Resources in Megrated Resource Planning, National Renewable Energy Laboratory, NREL/lP4626436.
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Qiscussion
Assessing the costeffectiveness of DSM and supplyside program options occurs during the screening analysis phase of the IRP process. Below we have described five widely used "standard practice" DSM costeffectiveness tests. We have focused on demandside options because many analysts are unfamiliar As . w i t h any BIC ratio test, options with ratios with the technical and policy problems of DSM ~ p t i o n ~ greater than or equal to one are considered economicallyjustified. The following BIC formulas, along with detailed idormation related to DSM analyses, can be found in EPRI's Principles and Practice of DemandSide Management (EPRI 1993).
Participant Test: Pa rficipant Perspective
The Participant Test provides a measure of the quantifiable benefits and costs of a DSM program to a tygical participating customer; it does not consider impacts on the utility. The intent of this perspective is to measure the economic and financial characteristics inherent to a program with the purpose of attracting customers. The benefits to the participant are equal to the sum of any participant incentives paid, any reduction in bills, and any federal or state tax deductions or credits. Participant costs include any other outofpocket costs associated with the particular program. The Participant Test can be expressed as follows: Participant Test = B, f C,,
Bp = CNi=r { [Ii i (ai * CRJ] f (1 C, = ENizl {DC, + (1
(423)
+ d)'}
+ d>i}
Where:
BP C P Ii
B i
= participant benefit = participant cost
= = = = = =
CR, DCi d
N
incentives received by participant in year i participant change in electricity use in year i consumer electricity rate in year i direct costs of consumer's participation in year i discount rate number of years.
For example, consider a residential DSM program involving energyefficient dishwashers, where the utility company offers a onetime $200 rebate when its residential customers purchase energyefficient dishwashers at $600 (assume standard dishwashers can be salvaged at $100, thus, the incremental consumer participation cost is $500). The washers have a 10year life span and save 1000 kWh per year. In addition, assume a real discount rate of 6% and a constant dollar electricity rate (consumer's cost) of $0.08 per kWh over the entire 10year period. The Participant Test for this example is calculated as follows:
Participant Test = $788.80 + $500 = 1.58 Where:
B, = $200 i E1oi=l [(LOO0 kWhlyear * $O.O8/kWh) + (1 C , = $600  $100 = $500.
(424)
+ 0.06)'] = $788.80
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The participant test B/C ratio is greater than 1; thus, this program is costeffective from the participant¡¯s perspective. Because the participant test is an indication of the attractiveness of this program to customers, it is also an indication of the general level of program participation that can be expected.
Total Resource Cost Pest: Utility and Ratepayer.Perspective
The Total Resource Cost (TRC) Test provides a measure of the net resource expenditure of a DSM program ftom the point of view of the utility and its ratepayers as a whole. Resource benefits include the utility¡¯s avoided supply costs. Resource costs include the utility¡¯s and participants¡¯ direct costs. Because the utility and its ratepayers are taken as a whole, incentives and revenue changes are ignored. This test is also called the All Ratepayers Test. The TRC Test can be expressed as follows:
TRC Test = B, i C,, (425)
B, = CNi,l[(Bi * MCJ i (1 + d)¡¯]
C, =
cNi,l [(mi * UCJ+ (1 + d)¡®l
Where:
Bt
ct
fii
MC, DCj
uci
d N
= = = = = = = =
total resource benefit total resource cost participant change in electricity use in year i marginal cost of electricity in year i direct costs of consumer¡¯s participation in year i direct costs of utility¡¯s participation in year i discount rate number of years.
Assume the same parameters as those in the Participant Test example. In addition, assume a onetime direct utility participation cost of $100 in the startup year and a constant dollar marginal electricity cost (utility¡¯s cost) of $0.06 per kWh. The marginal cost should include the utility¡¯s avoided energy and capacity costs for generation, transmission, and distribution. The TRC Test for this example is calculated as follows. TRC Test = $441.60 + $600 = 0.74 where:
B, = C1Oi=, [(1,000 kWh/year * $O.OB/kWh) + (1 + 0.06)¡¯] = $441.60 C, = $500 + $100 = $600
(426)
Because the TRC test BIC ratio is less than 1, this DSM program is not economical from the combined perspectives of the utility and the ratepayers. It is important to note that if the incentives paid in a DSM program are exactly equal to the full cost of the equipment to the customer and there are no tax credits, the TRC Test and the Utility Cost Test (described later) yield the same results.
Ratepayer impact Measure Test: Nonparticipant Perspective
The Ratepayer Impact Measure (RIM) Test is a measure of the difference between the change in total revenues paid to a utility and the change in total costs paid by a utility. If the change in revenues is larger or smaller than the change in total costs (RI),then rate Levels have to change because of the program. This test is also called the Nonparticipant Test. The RIM Test can be expressed as follows:
RIM Test = Br + C,,
B, = ENizl [(iEi * MCJ
4
(427)
(1 + a)¡¯]
Cr = CNi,l{ (Ii + UCi + a i * C R i ) + (1 + d)i}
Where:
Br Cr
AEi
MC,
= = = =
=
Ii
UC,
d N
CR,
= = =
=
ratepayer resource benefit ratepayer resource cost participant change in electricity use in year i marginal cost of electricity in year i incentives received by participant in year i direct costs of utility¡¯s participation in year i consumer electricity rate in year i discount rate number of years.
For example, assume the same parameters as those in the TRC Test example. The RIM Test for this example is calculated as follows.
RIM Test = $441.60 f $888.80 = 0.49
(428)
Where:
B, = C1oi=l [(l,OOO kWh/yex * $0.06/kWh) (1 + 0.06)¡¯] = $441.60 C,= $200 + $100 + [(1,000 kWWyear * $O.OS/kWh) f (1 + 0.06)¡¯]= $888.80
cloi=l
+
The RIM Test B/C ratio is less than 1, thus, this DSM program is not costeffective from the ratepayer perspective because rate levels will increase as a result of this program. If consumer electricity rates are higher than marginal electricity costs, few programs pass this test. In dollar terms, the two largest components of this test are the changes in supply costs and the changes in total revenues. If rates are higher than marginal costs, the benefit of avoided supply costs is overshadowed by the cost of revenue losses.
Utility Cost Test: Utility Perspective
On the utility side, a DSM program could alter the daily operation of generation and, ultimately, could
change the generation, transmission, and distribution systems and administration practices. The benefits from the utility perspective are the avoided supply costs resulting fkom program implementation. The costs associated with the program can be characterized as customer incentives and direct utility participation costs.
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The utility perspective can be expressed as follows:
UC Test = B, f C,,
B, = CNi,l[ ( a * MCJ , 4 (1 + d)¡¯]
(429)
C, = CNi,l [(Ii + UCJ i (1
+ d)¡¯]
Where:
B u
c u
fii
MC, Ii UC,
= = = =
d N
= = = =
utility benefit utility cost participant change in electricity use in year i marginal cost of electricity in year i incentives received by participant in year i direct costs of utility¡¯s participation in year i discount rate number of years.
For example, assume the same parameters as those in the RIM Test example. The Utility Cost (UC) Test for this example is calculated as follows.
UC Test = $441.60 t $300 = 1.47
(430)
Where:
€3, = [(1,000 kWNyear C , = $200 $100 = $300.
cloi=l
+
* $O.OGkWh) + (I + 0.06)¡¯] = $441.60
Because in the long run, total costs to the utility (RR) equal total revenues (total energy bills paid by customers), this test measures the change in the total amount paid in utility bills across all customers. In general, a UC Test ratio of less than 1 indicates an increase in the utility¡¯s cost due to the implementation of a DSM program. This results in an increased electricity rate that will subsequently increase the total amount paid in utility bills. Similarly, a UC test ratio greater than 1 indicates a decrease in the utility¡¯s cost, which will subsequently decrease the total amount paid in utility bills (i.e., lowers customer rates).
Societal Test: Sociefal Perspective
The Societal Test is a measure of the net benefits of a DSM program from the point of view of society as a whole. This test attempts to capture all benefits and costs of a DSM program, including externalities. It is generally agreed that external benefits and costs are difficult to identify and quantify. Refer to the Electric Power Research Institute¡¯s (EPRI¡¯s) Principles and Practice of DemandSide Management (EPRI 1993), or the Externalities subsection in Section 5 , for discussions regarding incorporating externalities into DSM planning. Benefits associated with the societal perspective include direct and indirect benefits. The direct benefits are the avoided supply costs, whereas the indirect benefits include factors such as increased labor or economic activity and environmental benefits. Direct costs include all consumer and utility expenses associated with the program, whereas indirect costs include items such as decreased labor or economic activity and environmental costs.
The Societal Test can be expressed as follows:
B/C (societal) = B,
+ C, + (1 + d$)
(431)
C, = CNi,l{ [DCi + UC, + (C,&
Where:
= societal benefit = societal cost
= change in energy use in year i for fuel j
= marginal cost of energy in year i = direct costs of consumer¡¯s participation in year i
=
direct costs of utility¡¯s participation in year i
= external or indirect benefits in year i
= external or indirect costs in year i = societal discount rate (usually assumed to equal the utility¡¯s discount rate) = number of years.
Since its beginnings, DSM has evoked arguments concerning the appropriate screening analysis criteria in the selection of programs. A large portion of the debate pits the advocates of the RIM test against the advocates of the TRC test. Actually, the selection of DSM programs requires consideration of both tests because DSM programs need to address the twin goals of efficiency and equity.
EPRI proposes the following sequential methodology for the selection of DSM programs:
Eliminate all programs that do not pass the TRC Test. Implement all programs that pass the RIM Test. Redesign the remaining programs that pass the TRC Test but fail the RIM Test, to minimize their impact on nonparticipants. The explanations and definitions provided in this section for the use of B/C analysis with IRP have been brief. This section is included in the manual to provide analysts with an awareness of IRP and B/C analyses in actual practice. For more information, please refer to PrincipEes and Practice of DemandSide Management (EPRI 1993).
Consumer/Producer Surplus
Introduction
The implications of research, development, and demonstration (RD&D) and other policy actions of the DOE Office of Energy Efficiency and Renewable Energy extend beyond the results that may be recorded in a conventional economic analysis, which usually is confined to evaluating the direct impacts on the provider and user of an energy service. There are potential environmental impacts, national security
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benefits and issues, regional and/or rural economic development impacts, national economic benefits (such as consumers¡¯ and producers¡¯ surplus), and impacts on other federal, state, or local programs. In voluntary markets, it is generally accepted that some consumers are willing to pay more for a given quantity of a product than they must pay. The difference between the total amount of money a consumer would be willing to pay for a given quantity of a commodity minus the total expenditures that are necessary to acquire that quantity of the commodity is called the conxurner¡¯s surpEus (L,eftwich and Eckert 1985). Conversely, it is generally accepted that some producers are willing to accept less for a given quantity of a product than they receive. The difference between the total amount of money a producer receives for a given quantity of a commodity minus the total expenditures that are necessary to produce that quantity of the commodity is called the producer¡¯s surplus.
Discussion
Figure 42 illustrates the concepts of consumer surplus and producer surplus using traditional demand and supply curves.
Figure 42. Consumer and producer surplus
At the market position (P*,Q*), the market clears for the quantity Q*, selling for the price P? The area abQ*O describes the total value the consumer holds for this particular quantity of this commodity. The total amount of money paid for the commodity is P*bQ*O. The value held by the consumer for this quantity of the commodity (Q*) over and above the total amount paid is abP*, or the consumer surplus. Because this is a voluntary market, the seller¡¯s costs and normal profits27are included in the seller¡¯s supply curve. Otherwise, the seller