A History of Discount Rates and Their Use by Government Agencies

A History of Discount Rates and Their Use by Government Agencies Richard O Zerbe Jr Xi Han David Layton Tom Leshine October 2002 1.0 Introduction This report reflects a history of the use of discount rates by government agencies along with a history of the values of real interest rates The major conclusion of this report is that there is little consistency in government decisions to use or not to use discount rates or in their choice of particular rates when they are used This article is organized as follows: section two deals with the concept of discount rates; section three examines various discount rates used by government agencies; section four analyzes why discount rates differ among government agencies; and section five looks at the history of real interest rate in U.S We not suggest here what discount rates should be used 2.0 What are Discount Rates? Discount rates reflect simply the particular use of interest rates to find the earlier value of expected returns Interest rates are used by lenders and borrowers to determine the amount of some future payment.1 Thus if P is the amount borrowed today and r is the interest rate, then the future value F, or the amount to be paid back at time T, will be given by F = P(1+r)T (1) The interest rate r is called the discount rate when it is used to solve for P given the other values Thus in using the following equation (2) the practice is called discounting and r is said to be the discount rate2 A history of interest rates from prehistoric times to 1990, including a history of rates in the United States from 1700's through 1990, may be found in Homer and Sylla (1998) Equation assumes yearly discounting, i.e., the interest rate is paid yearly Economists often use continuous discounting as it lends itself to more elegant mathematics Then the formula will be P =F/(e rt) where e is the natural log and r and T as before However, the difference in the final results is not large even if the time period is long For example the present value of a future sum discounted continuously over a 500 year-period will be about 80% of the present value calculated using yearly discounting If the future value were 100 trillion, the present value difference would be only about $8,000 as the discounted figures would both be in the $30,000 range P = F/(1+r)T (2) Thus the use of discount rates must be as old as the use of interest rates We will focus here simply on the use of such rates in more modern times and in particular their use by government agencies Interest rates and thus discount rates may be expressed in real or nominal terms Nominal rates are market rates which by their nature contain an expected inflation factor Real rates are nominal rates from which expected inflation (in practice usually actual inflation) has been removed The real rate R is related to the nominal rate r as through the expected inflation rate, Ie as follows: R = (1+ r)/(1+Ie) -1 (1) which may be expressed approximately as R ≅ r - Ie (2) Thus if the nominal interest rate is 7%, expected inflation is 2%, the real interest rate R would be 4.90% or approximately 5% The conceptually correct procedure is to use real rates to discount real benefits and costs (constant-dollar values) and to use nominal rates to discount nominal benefits and costs (current-dollar values) To mix real with nominal values is to allow inflation in one part of the calculation but not in the other 3.0 Rates for Government Agencies 3.1 Federal Agencies There is little consistent practice in government both in the choice of a particular discount rate, and in the decision of whether or not to use discount rates This inconsistency is found across different levels of government, among different government agencies at the same level, and across time within the same agency Thus not all Federal agencies use the same discount rates, nor they always use discounting at all Bazelon and Smetters (1999, p 219) note that, “In many cases, federal agencies not discount ” and further, "congressional cash-based budget planning does not discount either." Federal agencies often treat a dollar spent now exactly the same as a dollar spent next year (e.g yearly budgets, mandatory spending) Further, "changes in spending beyond the five or ten-year budget window are essentially discounted at an infinite rate3." The following then briefly goes over the history of discount rates used by different federal agencies I Discount Rates Used by Office of Management and Budget (OMB) According to the OMB Circular No A-94, dated March 27, 1972 , "Discount Rates to be Used in Evaluating Time-Distributed Costs and Benefits" 4, a real rate of 10 percent was recommended by OMB for use from March 27, 1972 until October 29, 1992 This rate represents an estimate of the average rate of return on private investment, before taxes and after inflation This Circular applies to all agencies of the executive branch of the Federal Government except the U.S Postal Service And the 10 percent real discount rate applies to the evaluation of Government decisions concerning the initiation renewal or expansion of all programs or projects, other than those specifically exempted (decisions concerning water resource projects, the Government of the District of Columbia, and non-Federal recipients of Federal loans or grants) There have been two additional exceptions to the use of this rate according to Lyons (1990) The first is that agencies were allowed to use a different rate when an alternative rate can be justified However, the acceptable basis for using a different rate are not spelled out The second exception to the 10 percent rule has been lease or purchase decision, for which the OMB Circular No A-104, dated June 14, 1972, "Comparative Cost Analysis for Decisions to Lease or Purchase General Purpose Real Property", specified a real rate of percent This rate represents an estimate of the internal rate of return on general purpose real property leased from the private sector, exclusive of property taxes and expected inflation This rate is influenced by IRS tax treatment of real property and by separate handling of property taxes in Circular A-104; and it is specific to lease-or-purchase decisions and is not comparable to before tax rates of return that the OMB specified in Circular A-94 In October 1992, the OMB Circular No A-94 was extensively revised According to the OMB Circular No A-94, dated October 29th, 1992 ,"Guidelines and Discount Rates Changes to the budget in spending beyond 5-10 years (depending on the structure of the budget) in the future often not enter the calculations and Bazelon notes that this basically discounts the changes infinitely From 1968, the Bureau of the Budget (BOB) had undertaken a review of the theoretical foundations for discounting and issued Circular A-94 in June, 1969, in which a real discount rate of 10% is set for all government agencies except those concerned with water resources This means that a real rate of 10% was recommended by BOB from 1969 until 1972 for Benefit-Cost Analysis of Federal Programs", two basic types of discount rates have been specified: (1) a discount rate for public investment and regulatory analyses; and (2) a discount rate for cost-effectiveness, lease-purchase, internal government investment and asset sale analyses For the base case of public investment and regulatory analyses, OMB now suggests a real discount rate of percent This rate is said by OMB to approximate the marginal pretax rate of return on an average investment in the private sector in recent years For the cost-effectiveness, lease-purchase, internal government investment and asset sale analyses, OMB discount rates are based on interest rates on Treasury Notes and Bonds with maturities ranging from to 30 years The rate used may be either nominal or real, depending on how benefits and costs are measured Analyses that involve constantdollar costs should use the real Treasury borrowing rate on marketable securities of comparable maturity to the period of analysis This rate is computed using the Administration's economic assumptions for the budget, which are published in January of each year Real Treasury rates are obtained by removing expected inflation over the period of analysis from nominal Treasury interest rates The history of nominal interest rates used by OMB is presented in Table These nominal rates are used for discounting nominal flows, which are often encountered in lease-purchase analysis And the history of real interest rates used by OMB is presented in Table These real rates are used for discounting real (constant-dollar) flows, as is often required in costeffectiveness analysis HISTORY OF PAST YEARS RATES * (from the annual budget assumptions for the first year of the budget forecast) Table 1: Nominal Treasury Interest Rates Forecast Date February 1992 February 1993 February 1994 February 1995 February 1996 February 1997 February 1998 February 1999 February 2000 February 2001 February 2002 3-Year 6.1 5.6 7.3 5.4 5.8 5.6 4.7 5.9 5.4 4.1 5-Year 6.5 5.3 7.6 5.5 5.9 5.7 4.8 5.4 4.5 7-Year 6.7 6.3 5.5 7.7 5.5 5.8 4.9 5.4 4.8 10-Year 6.7 5.7 7.9 5.6 6.1 5.9 4.9 6.1 5.4 5.1 30-Year 7.1 6.8 5.8 8.1 5.7 6.3 6.1 6.3 5.3 5.8 Table 2: Real Treasury Interest Rates Forecast Date 3-Year 5-Year 7-Year 10-Year 30-Year February 1992 2.7 3.1 3.3 3.6 3.8 February 1993 3.1 3.6 3.9 4.3 4.5 February 1994 2.1 2.3 2.5 2.7 2.8 February 1995 4.2 4.5 4.6 4.8 4.9 February 1996 2.6 2.7 2.8 2.8 February 1997 3.2 3.3 3.4 3.5 3.6 February 1998 3.4 3.5 3.5 3.6 3.8 February 1999 2.6 2.7 2.7 2.7 2.9 February 2000 3.8 3.9 4 4.2 February 2001 3.2 3.2 3.2 3.2 3.2 February 2002 2.1 2.8 3.1 3.9 *These are the rates that have appeared annually in Appendix C of OMB Circular A-94 since 1992.The discount rates in Appendix C are drawn from OMB's assumptions for interest rates used in the budget II Discount Rates Used by Department of Energy (DOE) Since 1996, the Department of Energy reports its discount rate yearly The DOE discount rate is based on long-term Treasury bond rates averaged over the previous 12 months The nominal, or market rate, is converted to a real rate using the projected rate of general price inflation from the Economic Report of the President's Council of Economic Advisors, to correspond with the constant-dollar analysis approach that is used in most federal life-cycle cost (LCC) analyses Federal agencies and contractors to federal agencies are required by 10 CFR 436 to use the DOE discount rate when conducting LCC analyses related to energy conservation, renewable energy resources, and water conservation projects for federal facilities According to NISTIR 85-3273-10, October 1995, the Department of Energy uses a real discount rate of 4.1 percent or a nominal discount rate of 7.6 percent for 1996 (the projected rate of general price inflation was 3.4%) According to NISTIR 85-3273-11, July 1996, the Department of Energy uses a real discount rate of 3.4 percent or a nominal discount rate of 6.6 percent for 1996 (the projected rate of general price inflation was 3.1%) According to NISTIR 85-3273-12, April 1997, the Department of Energy uses a real discount rate of 3.8 percent or a nominal discount rate of 6.9 percent for 1997 (the projected rate of general price inflation was 2.9%) According to NISTIR 85-3273-13, April 1998, the Department of Energy uses a real discount rate of 4.1 percent or a nominal discount rate of 6.6 percent for 1998 (the projected rate of general price inflation was 2.4%) According to NISTIR 85-3273-14, July 1999, the Department of Energy uses a real discount rate of 3.1 percent or a nominal discount rate of 5.7 percent for 1999 (the projected rate of general price inflation was 2.5%) According to NISTIR 85-3273-15, April 2000, the Department of Energy uses a real discount rate of 3.4 percent or a nominal discount rate of 6.3 percent for 2000 (the projected rate of general price inflation was 2.8%) According to NISTIR 85-3273-16, April 2001, the Department of Energy uses a real discount rate of 3.3 percent or a nominal discount rate of 6.1 percent for 2001 (the projected rate of general price inflation was 2.7%) According to NISTIR 85-3273-17, April 2002, the Department of Energy uses a real discount rate of 3.2 percent or a nominal discount rate of 5.6 percent for 2002 (the projected rate of general price inflation was 2.3%) The following table sums up all the discount rates used by DOE from 1996 until 2002: Table 3: Discount Rates Used by DOE Year 1996 (1995 analysis) 1996 (1996 analysis) 1997 1998 1999 2000 2001 2002 Official Document Real Discount Rate Nominal Discount Rate Projected 10-year Average Inflation Rate NISTIR 85-3273-10 4.1% 7.6% 3.4% NISTIR 85-3273-11 3.4% 6.6% 3.1% NISTIR 85-3273-12 NISTIR 85-3273-13 NISTIR 85-3273-14 NISTIR 85-3273-15 NISTIR 85-3273-16 NISTIR 85-3273-17 3.8% 4.1% 3.1% 3.4% 3.3% 3.2% 6.9% 6.6% 5.7% 6.3% 6.1% 5.6% 2.9% 2.4% 2.5% 2.8% 2.7% 2.3% III Discount Rates Used by Other Federal Agencies The Congressional Budget office (CBO) since 1990 has used a real rate of 2% (Thompson and Green, 1998; Bazelon and Smetters, 1999, p222) Analysts are directed to perform sensitivity analysis using plus and minus percent around this rate (Bazelon and Smetters, 1999, p222) The General Accounting Office (GAO) generally uses lower discount rate than the OMB recommended rates based on the average nominal yield on treasury debt minus the inflation rate They recommends the use of a very low discount rate when analyzing policies with large intergenerational effects involving human life They use especially lower rates (close to zero) for projects with strong intergenerational health effects The logic seems to be that the individual's growth in productivity would offset the interest rate Thus if the discount rate is 2.5% and the productivity growth rate is 2%, the GAO would suggest what is usually called a net discount rate of 0.5% Water resource projects, contracting out, and federal energy management programs are exempt from GAO and OMB guidelines These projects fall under different regulations Water resource projects have been justly criticized in the past for using nominal interest rates with real dollar benefits and costs (see Lyons, pS-31) The current guidance for water resource projects is the approved Economic and Environmental Principles and Guidelines for Water and Related Land Resources Implementation Studies (Principles and Guidelines, 1983) It requires the agencies to calculate present values of projects using the discount rate established annually for the formulation and economic evaluation of plans for water and related land resources plans And the guidance for federal energy programs can be found in the Federal Register of January 25, 1990, and November 20, 1990 (Volume 55)8 In these guidances, the Department of See Footnote Bazelon and Smetters (1999) mention that "the GAO guidelines recommend the use of a very low discount rate when analyzing policies with large intergenerational effects involving human life" And in GAO, 1991, "the guidelines note that if the value of human life increases with increases in productivity, the effective discount rate for evaluating the present value of future human lives is roughly zero" Implementation studies of the following agency activities are covered by these principles: (a) Corps of Engineers (Civil Works) water resources project plans; (b) Bureau of Reclamation water resources project plans; (c) Tennessee Valley Authority water resources project plans; (d) Soil Conservation Service water resouces project plans In the Federal Register of January 25, 1990, the Department of Energy proposes to amend 10 CFR part 436, which sets forth guidelines applicable to Federal agency in-house energy management programs In the Federal Register of November 20, 1990, the Department of Energy gives notice of final amendments to 10 CFR part 436 to update the guidelines applicable to Federal agency in-house energy management programs Energy (DOE) states that measuring the interest rate on U.S Treasury bonds and removing the effects of inflation is the appropriate procedure for setting a market-based discount rate to be used in performing life cycle cost analyses for purposes of estimating and comparing the cost effects of investing in greater energy efficiency in Federal buildings The discount rate will be set by DOE for one-year intervals coinciding with the Federal fiscal year, and the supporting tables for use in life cycle cost analysis are to be made available in an annual supplement to the Life Cycle Costing Manual for the Federal Energy Management Program (NIST 85-3273) issued at the beginning of each fiscal year9 The rates used by the Corp of Engineers have varied from as low as 2.5% to as high as 8.75% over the period from 1957 through 1980 (Zerbe and Dively, 1994, p277-278.) There also have been peculiar practices required of the Army Corp and the Bureau of Reclamation by which real rates are to be used with nominal benefits and costs This practice of combining real and nominal values makes no sense and economists at the Corp and at the Bureau of Reclamation with whom we (Zerbe) have talked recognize this We are unable to determine the origin of this practice In short, there is a lack of consistency for Federal government use of discount rates The range of federal rates used by federal agencies is then from 2% to 7% in real terms, though the effective real rate used by the Bureau of Reclamation and the Corp of Engineers could be even higher when market rates , which include an expected inflation component, are applied to expected real benefits and costs In so far as government rates are based on Treasury bond rates which is the case with OMB lease purchase decision and with the rates used by the Bureau of Reclamation and the Corp of Engineers, it is recommended that bonds be chosen whose terms correspond with the time period of the project This means that longer lived projects would be evaluated with larger interest rates The yields on Treasury instruments (over the period from January 1979 to February 2002) would yield a low real rate of 2.1% in February 2002 on 3-year notes and a high real rate of 7.9% in February 1982 for 30-year projects (the current OMB circular A-94) See the previous Part "II Discount Rates Used by Department of Energy (DOE)" Such rates normally increase with time due to inflation risk If this logic is extended to very long lived projects it suggests quite large discount rates.10 3.2 Rates Used by State and Municipal Governments As far as we can discern no one has systemically collected information for discount rates used by various state governments There appears to be no general knowledge of how the use of discount rates vary across state governments or what rates they use, although this knowledge can be gathered state by state 11 The justification for government rates has ranged from using the rate on government bonds (the government cost of capital) to using the rate on private capital to using the social rate of time preference Little has been published about municipal use of discount rates Consequently we attach an Appendix that contains an unpublished survey of municipal rates that some of us undertook (Zerbe and Dively, 1993) A random sample of 72 cities with populations over 100,000 were asked a series of questions of their use and understanding of the use of capital budgeting and discount rates About 37% reported they use such rates and as many as 46% may use them indirectly through consultants That is, over half of municipal governments with populations over 100,000 not use discount rates in their planning The roughly 40% of municipal governments that use rates generally use a real rate in the 2.5% - 3.5% range.12 The only variable we found that is correlated with the use of discount rates is that cities with independently elected officials are more likely to use (and to understand) discount rates than other cities 13 Some municipal government consciously avoid benefit cost analysis and the use of discount rates Interesting, expressed rationale in many cases is the desire to make decisions on a purely political basis which they find is complicated by the use of benefit cost analysis and the attendant use of discount rates 10 See Appendix C, OMB Circular No A-94, Tuesday, August 6, 2001 See for example, "Manual for Discounting Oil and Gas Income", Texas Comproller of Public Accounts, 1999 12 Dively, Dwight D., Zerbe, Richard O., “Benefit Cost Analysis In Theory and Practice”, HarperCollins College Publishers, 1994 13 Technically one says that having independently elected officials increases the log odds of using discount rates by the amount given by the beta coefficient (Judge et al, ) (See betas in Appendix tables) Differences were also tested using chi-square tests with similar results 11 4.0 Why Rates Differ Among Agencies The basis for the choice of discount rates varies among agencies and appears to have been significantly influenced by academic literature at the Federal level The issues that have motivated these debates involve questions of whether risk should be treated differently for government investments than for private investments, and whether the rate of time preference on the one hand or the opportunity cost of capital on the other is the more appropriate for government rates In the case of municipal governments, however, the driving force appears to simply be the rate the municipality must pay on its bonds There has been a debate in the economics literature for some time whether rates should reflect the social rate of time preference (SRTP) or the opportunity cost of capital (OCR) The SRTP is the rate at which individuals are willing to trade off present for future consumption Some agencies base their choice of rates on a social rate of time preference (e.g., Congressional Budget Office, and General Accounting Office) This rate is commonly equated with the risk free rate of return on government bonds, though there is no definitive SRTP rate.14 Other federal agencies such as OMB, base their rates on the price of capital in the private sector-the before tax rate of return to private capital Others, most commonly municipal governments, base their rate on their own costs of capital which they see as the interest they must pay to issue bonds so that in practice those that base their rate on the SRTP and pragmatically on the cost of generating government capital tend to choose about the same rates The OCR rates tend to be significantly higher than the rates based on the yield on government bonds so that OCR rates are generally significantly higher than rates used by municipalities or rates based on the SRTP A parallel debate has concerned whether or not government discount rates should include a risk premium as they in the private sector In general, private rates of return are said to equal the risk-free rate plus a risk premium depending on the market risk of the equity The return to equities above government bills is said to have averaged percentage points a year during the past century, an astronomical difference when compounded over time (Bazelon and Smetters 1999) 15 Bazelon and Smetters conclude 14 Individuals show quite different ranges of time preference in revealed choice experiments depending on the type of decision they must make (e.g consumption versus saving for retirement) and on their level of education CITES) 15 Bazelon is the Principal Analyst, Congressional Budget Office, Washington, D C 10 Bond rating The use of quantitative financial methods is often discussed as one of the important factors in setting a jurisdiction's bond rating In order to test this hypothesis, bond ratings for the cities in the sample were collected and analyzed The August 1991 ratings by Moody's Investors Service were used for this purpose Ratings were not available for all of the cities since some cities have not issued debt recently There is not significant difference in using a discount rate between the half of cities with the higher bond rating and the half with the lower (sig nificant at 68% level) However, the sample size for this variable is only 42 and the difference in discount rate usage is, however, close to significance between the cities with a bond rating of A or better and those with a B or worse rating (significant at 11%) The cities with lower bond ratings may be more likely to use a discount rate (There is a weak correlation between (r= 0.187) with lower bond ratings.) There is a possibility that cities with a lower bond rating are using more formal capital budgeting techniques to improve their rating or that there capital constraints are greater and they are attempting to use them more efficiently Higher bond ratings are thought to lower interest rates paid on debt, which should also lower the cost of capital and therefore also probably lower discount rates (Zerbe ,1993) However, the survey revealed that this effect is very modest at least for our sample, and not statistically significant, since the cities with Aa ratings or higher used an average discount rate of 7.82 percent, compared 7.92 percent for cities with lower bond ratings Presence of independently elected officials Some cities have independently elected finance officials, such as an auditor, comptroller, treasurer, or revenue commissioner It might be expected that the presence of such officials would increase the use of discount rates since there would be a higher standard of review of proposals This higher standard often would result because of 36 discussions between different finance staffs: one reporting to the mayor or city manager, and one reporting to the independently elected official The survey results support this hypothesis Eight of the cities surveyed have independently elected finance officials, and six of the eight (75.0 percent) use discount rates This use of discount rates is double the rate for the sample as a whole The difference in discount rate usage between cities with and without independently elected officials is significant at the 1.6% level 27 Thus, there appears to be a statistically significant difference in the use of discount rates depending on the presence of independently elected officials.28 Perhaps also the independently elected official crates a single accountable post which is responsible for decision making, thus increasing the incentive to make the best decision Geographical location Cities in some sections of the country might make more extensive use of discount rates because of prevailing practices or the presence of educational institutions emphasizing such techniques The survey revealed some such geographical differences Discount rates seem to be used more often by cities in the West Coast, Great Lakes, and Middle Atlantic states Discount rates seem to be the least used by cities in the New England and Southern states The surveys revealed no obvious reason for these differences As a more sophisticated statistical approach a logit equation was run in which the dependent variable was a binary variable, the use or non-use of the discount rate In a logit equation the coefficients represent the effect of the variable on the log of the oddshere the odds of using a discount rate In each equation there were two independent variables; independently elected financial officials was run separately with population, 27 This is the significance level assuming the two groups have the same variance assuming unequal variances the level of significance is better than 5% (at 0.03) 28 The cities with independently elected officials tend to be larger than those without and this may also play a role 37 population growth and city age In all of these two variable runs, independently elected financial officials is significant at better than the 5% level The cities growth rate is close to significance at the 11% level, and the other variables are not significant 29 The Tables in the Appendix report the statistics for three of the runs with two variables The major result of the data analysis to compare differences in means is that cities with independently elected officials are more likely to use (and to understand) discount rates than other cities.30 A test of the differences in means suggests that cites with higher population growth rates are less likely to use discount rates Older cities may be more likely to use discount rates, but cities with larger populations may be more likely to use them The presence of utilities and bond rating appear not to be correlated with the use of discount rates The survey also revealed that discount rates appear to be used more frequently in cities in the West Coast, Great Lakes and Middle Atlantic states They are least used by the New England and Southern states 31 The survey revealed no obvious reason for these differences Summary Most municipal governments may not use discount rates and appear not to understand present value analysis A number of these were rather forthright about political concerns dominating investment decisions and gave as a reason for not using discount rates that their use would make politically based decisions more difficult This 29 When all variables are entered only 42 observations are available, and the small number of observations make it less likely that significant relationships will be exhibited by the data For the logit equation with all variables entered none of the variables reaches significance at the 10% level, although the presence of independently elected officials was close to significance (at the 13% level), and was followed in significance by the percentage population growth rate (at the 28 level ) A run without bond rating allows the use of the full sample of 72 and in this run independently elected officials is significant but no other variables 30 Technically one says that having independently elected officials increases the log odds of using discount rates by the amount given by the beta coefficient (Judge et al, ) (See betas in Appendix tables) Differences were also tested using chi square tests with similar results 31 A variable that might be of interest is the level of schooling of city officials 38 explanation is consistent with the major finding that the presence of independently elected finance officials significantly increases the use of discount rates and the understanding of present value analysis Such officials may reduce the discretion of others in an administration It seems possible that the existence of such officials is costeffective from a financial perspective A potentially important finding is that cities with independently elected finance review officials are more likely to use a discount rate, suggesting the possibility that the presence of these review officials produces a higher standard of analysis What this study strongly suggests most strongly is that there is substantial opportunity for improving the efficiency of capital budgeting by municipal governments It also suggests that one way to this is to have an independently elected financial official Of the approximately 40% of municipal governments that use discount rates almost all use some variant of the cost of capital to determine the rate The range of rates they exhibit, at least at the point in time we examined, is almost entirely within the range we have determined to represent the range for the real after tax return to government bonds which in turn appears consistent with social rate of time preference rate suggested by economic theory (Zerbe and Lesser, 1994) Thus, municipal use of discount rates is more consistent among municipalities and more consistent with theory than are rates used by different divisions within the Federal government The Federal Office of Management and the Budget (OMB) (in circular A-94) at the time this survey was written recommended and often required a real (inflation adjusted) rate of 10%, far higher than theory would suggest.32 Congressional agencies use other rates (Lyons, 1990) A complete explanation of why certain cities use discount rates would require further research Such research might focus on the role of state laws in influencing city budget practices, the form of city government, a more comprehensive review of the types 32 Since this survey OMB has reduced its recommended real rate to 7% 39 of capital projects undertaken by cities, and on the educational backgrounds of budget officers in different parts of the country There is no unanimity among cities regarding the frequency with which the discount rate should be revised or reexamined We found no statistically significant relationship between population size and the probability of using a discount rate, although there is some suggestion that there is a weak, positive correlation Older cities appear are more likely to use a discount rate We not know why older cities may be more likely to use a discount rate Cities that are growing faster are less likely to use discount rate, and this appears to be due mainly to the fact that older cities are more slowing growing and are more likely to use a discount rate than newer cities Neither the importance of city utilities nor the cities bond rating are correlated with the use of a discount rate 40 Table Results of Discount Rate Survey City Albuquerque, NM Anaheim, CA Anchorage, AK Arlington, TX Atlanta, GA Baltimore, MD needed Baton Rouge, LA bond issue Birmingham, AL Boise, ID Boston, MA Bridgeport, CT Buffalo, NY Charlotte, NC Cincinnati, OH Columbus, OH Corpus Christi, TX Dallas, TX Dayton, OH needed Denver, CO needed Des Moines, IA Detroit, MI Eugene, OR needed Fort Wayne, IN Fresno, CA Hartford, CT Honolulu, HI Houston, TX Indianapolis, IN Use of Rate Nominal Rate No – Yes 9.00 Annually No – No – Yes 7.50 Continuously Yes 7.48 Real Rate – 4.00 Method for Setting Revision Current – return 2.5 Current – – cost 2.48 Current cost of capital Estimate by consultant Each – – funds on of – – capital As Yes 7.02 2.02 No – No No – 8.00 – – – – 3.0 – 8.00 – 3.0– Current – – – 7.75 – – – 2.75– – – – Current return on funds – – – As varies varies– Current cost of capital; As current return on funds – – Current return on funds – – As No Yes Annually No Yes Annually No No No Yes Yes No No Yes – – 8.50 – – 3.5 No No No No No Yes Annually – – – – – 7.50 – – – – – 2.5 – – – – Estimate by – – – – consultant – cost – capital of – – – – – – – – – – Bond yields for other cities 41 Jackson, MS Jersey City, NJ Kansas City, MO Knoxville, TN Lincoln, NE Little Rock, AR Los Angeles, CA Louisville, KY Madison, WI Memphis, TN Miami, FL No No No No Yes No Yes Continuously Yes Monthly No No Yes Annually – – – – 5.00 – varies – – – – – – – – – – – – – – Inflation rate Annually – Current cost of capital 8.00 3.0 Bond yields for other cities – – 7.00 – – 2.00 – – Estimate by – – consultant 42 Table Results of Discount Rate Survey (continued) Use of Rate City Milwaukee, WI Minneapolis, MN needed Mobile, AL Nashville–Davidson, TN New Orleans, LA Oakland, CA Omaha, NE Orlando, FL Paterson, NJ Peoria, IL Philadelphia, PA needed Phoenix, AZ Pittsburgh, PA Portland, OR needed Raleigh, NC Richmond, VA Rochester, NY needed Sacramento, CA needed Saint Paul, MN Saint Petersburg, FL Salt Lake City, UT San Diego, CA San Francisco, CA San Jose, CA Santa Ana, CA Seattle, WA needed Nominal Rate Real Rate Method for Setting Current cost Revision Yes Annually Yes 7.00 2.00 10.00 5.00 Taxpayer cost of capital As No No No No No No No No Yes – – – – – – – – varies – – – – – – – – – – – – – – – – – Long-term bond rate – – – – – – – – As No Yes Annually – 8.50 – 3.50 Current As – cost of of capital – capital; Yes 7.50 2.50 cost of existing debt Current return on funds No No Yes – – varies – – 3.75 – – Estimate by consultant – – As Yes 8.75 3.75– Current return on funds As No – No – No – No – Yes 7.50 Continuously – – – – 2.50– Current – – 2.50– cost of existing debt; inflation plus real rate – – Inflation plus real rate No Yes No – 7.50 – – – – cost of – – – – capital; – – As 43 Spokane, WA needed Stockton, CA Syracuse, NY Tucson, AZ Tulsa, OK needed Winston–Salem, NC Yonkers, NY Average Yes 8.50 3.50– No – No – Yes 10.00 Continuously – – 5.00– – Current return on funds Current – – cost of As – – capital, modified by risk of project Current return on funds As Yes varies No Yes Annually – 7.50 – – – 2.50– Bond yields for other cities 8.06 3.06 44 Table Characteristics of Responding Cities City Albuquerque, NM Anaheim, CA Anchorage, AK Arlington, TX Atlanta, GA Baltimore, MD Baton Rouge, LA Birmingham, AL Boise, ID Boston, MA Bridgeport, CT Buffalo, NY Charlotte, NC Cincinnati, OH Columbus, OH Corpus Christi, TX Dallas, TX Dayton, OH Denver, CO Des Moines, IA Detroit, MI Eugene, OR Fort Wayne, IN Fresno, CA Hartford, CT Honolulu, HI Houston, TX Indianapolis, IN Jackson, MS Jersey City, NJ Kansas City, MO Knoxville, TN Lincoln, NE Little Rock, AR Los Angeles, CA Louisville, KY Madison, WI Use of Rate No Yes No No Yes Yes Yes No No No No Yes No Yes No No No Yes Yes No No Yes No No No No No Yes No No No No Yes No Yes Yes No 1990 Population 384,736 266,406 226,338 261,721 394,017 736,014 219,531 265,968 125,738 574,283 141,686 328,123 395,934 364,040 632,910 257,453 1,006,877 182,044 467,610 193,187 1,027,974 112,669 173,072 354,202 139,739 365,272 1,630,553 741,952 196,637 228,537 435,146 165,121 191,972 175,795 3,485,398 269,063 191,262 Utilities Yes No Yes Yes Yes Yes No No No No No No Yes NA Yes Yes Yes No No No Yes No Yes Yes No Yes No No Yes No No No Yes No Yes No Yes 45 Table Characteristics of Responding Cities (continued) City Use of Rate Memphis, TN Miami, FL Milwaukee, WI Minneapolis, MN Mobile, AL Nashville-Davidson, TN New Orleans, LA Oakland, CA Omaha, NE Orlando, FL Paterson, NJ Peoria, IL Philadelphia, PA Phoenix, AZ Pittsburgh, PA Portland, OR Raleigh, NC Richmond, VA Rochester, NY Sacramento, CA Saint Paul, MN Saint Petersburg, FL Salt Lake City, UT San Diego, CA San Francisco, CA San Jose, CA Santa Ana, CA Seattle, WA Spokane, WA Stockton, CA Syracuse, NY Tucson, AZ Tulsa, OK Winston-Salem, NC Yonkers, NY No Yes Yes Yes No No No No No No No No Yes No Yes Yes No No Yes Yes No No No No Yes No No Yes Yes No No Yes Yes No Yes 1990 Population 610,337 358,548 628,088 368,383 196,278 510,784 496,938 372,242 335,795 164,693 140,891 113,504 1,585,577 983,403 369,879 437,319 207,951 203,056 231,636 369,365 272,235 238,629 159,936 1,110,549 723,959 782,248 293,742 516,259 177,196 210,943 163,860 405,390 367,302 143,485 188,082 Utilities No No Yes Yes NA No No No No No No No Yes Yes NA Yes Yes No No No Yes Yes Yes Yes Yes NA Yes Yes Yes Yes NA Yes Yes No No 46 References Forrester, John P “Municipal Capital Budgeting: An Examination”, Journal of Pubic Budgeting and Finance, 13, (2) Summer 1993 Havrilesky, Thomas, "New Evidence on Expected Long Term Real Interest Rates", Journal of Forensic Economics, Summer, 1988 Judge, George G R Carter Hill, William E Griffiths, Helmut Lutkepohl and TsoungChao Lee, An Introduction to the Theory and P{ractice of Econometrics, Second Editon, New York: John Wiley & Sons, 1988 Lind, R C., "Reassessing the Government's Discount Rate Policy in Light of New Theory and Data in a World Economy With Integrated Capital Markets," Journal of Environmental Economics and Management 18:S-8 - S-28 (1990) Lyons, Randolph, "Federal Discount Rate Policy, The Shadow Price of Capital and Challenges for Reforms", 18 Journal of Environmental Economics and Management S29-S50 (1990) Zerbe, Richard O Jr "Recommendations for Government Discount Rate Policy", No 92-1, Working Papers in Public Policy Analysis and Management, Graduate School of Public Affairs, (1992) Zerbe, Richard O Jr and Dwight Dively, Benefit Cost Analysis in Theory and Practice, Harper Collins (1994) Zerbe, Richard O Jr and Jonathan Lesser, "Discounting Procedures for Environmental and Other Projects: A Comment on Kolb and Scherage", JPAM, Winter, 1994 47 APPENDIX: LOGIT TABLES The following three tables show the coefficients for the two variable logit runs The sample sizes are 45, 44, and 45 for the three cases Variable Beta (coefficient) Standard Error Significance 1.68 0.9170 6.7% City Age -0.013 0099 18.7% Constant 24.11 18.91 20.2% Independently Elected Officials Variable Beta (coefficient) Independently Elected 1.79 Standard Error Significance 0.91 4.9% Officials Percent Growth Rate -3.91 2.43 10.8% Constant -0.57 0.39 15.0 Variable Beta (coefficient) Standard Error Significance 0.91 4.4% Independently Elected 1.84 Officials Population 1990 0004 0007 57% Constant -0.57 0.39 3.9 - 48 Appendix Nominal or real interest rates and are used to discount economic loss to present value in tort cases Nominal discount rates are market rates in current dollars, that is, unadjusted for inflation Real rates are nominal rates adjusted for inflation Similar definitions apply to nominal and real wage growth The relationships are approximately as follows:33 Market Rate (Nominal Rate) = Real Rate + Inflation (1) Real Rate = Nominal Rate - Inflation (2) As long as the market discount rate is used with nominal wages and the real discount rate is used with real wages, the use of the nominal and real rates will give the same answer as long as the inflation component is the same This may be seen by writing out the expression for the net present value of a wage stream: NPV = Wo(1 + g ) Wo(1 + g ) Wo(1 + g ) n + + (1 + r ) (1 + r ) (1 + r ) n (3) where g is the nominal or market growth wages in wages, Wois the wage one period before the initial period, and r is the nominal or market discount rate The nominal growth rate, G, will equal [(1 + I)(1 + g)]-1 where34 I is the Inflation rate and g is the real (inflation adjusted) growth rate Similarly, the nominal discount rate, r, will equal [(1 + I) (1+ r)]-1 where r is the real (inflation adjusted) discount rate 33 The exact definitions are, NR = [(1 +r)(1+I)]-1, and r = [(1 + R)/(1 + I] -1.where NR is the nominal rate, R is the nominal rate, r is the real rate of interest ,and I is inflation 34 Note that this equals I + g + Ig or approximately just I + g 49 The expression containing the inflation components will then divide out as long as the inflation components are the same in the denominator and numerator so that equation (4) may be written as: NPV = W o (1 + g ) (1 + r ) W o (1 + g ) + (1 + r ) 2 + W (1 + g ) (1 + r ) n n (4) That is, equations (3) and (4) shows that the NPV can equivalently be expressed in real or nominal terms 50 ... Interest rates and thus discount rates may be expressed in real or nominal terms Nominal rates are market rates which by their nature contain an expected inflation factor Real rates are nominal rates. .. real rates using actual, that is real rates of inflation Although Tables and report real rates using actual rates of inflation, as is the usual practice, this practice is incorrect Table 4: Realized... biased estimates of real discount rates and that net discount rates during this period may also be biased Several alternatives are possible We can examine expected instead of actual discount rates,