United States General Accounting Office GAO Report to the Chairman, Subcommittee on Transportation, Treasury, and Independent Agencies, Committee on Appropriations, House of Representatives June 2003 SAVINGS BONDS Actions Needed to Increase the Reliability of Cost-effectiveness Measures GAO-03-513 a June 2003 SAVINGS BONDS Actions Needed to Increase the Reliability Highlights of GAO-03-513, a report to the of Cost-effectiveness Measures Chairman, Subcommittee on Transportation, Treasury, and Independent Agencies, Committee on Appropriations, House of Representatives While the Treasury generally pays Treasury has several alternative vehicles for issuing debt to the public. A lower interest rates on U.S. Savings substantial majority of that debt is issued in the form of marketable Treasury Bonds than it does on other forms securities. U.S. Savings Bonds today account for about 3 percent of total of borrowing from the public, it Treasury securities outstanding. A majority of these bonds have lower also incurs substantially higher minimum denominations or face amounts than marketable Treasury administrative costs to issue and redeem the paper savings bond securities and generally pay lower interest rates as well, but provide the certificates. To determine whether same assurance of the full faith and credit of the United States, making them these higher administrative costs an alternative for investors unable or unwilling to pay the minimum exceed its interest rate savings, denominations of marketable Treasury securities. Savings bonds continue to Treasury’s Bureau of the Public be issued as paper certificates, rather than in the format of the “book entry” Debt uses a spreadsheet model to system for marketable Treasury securities; however, this increases the compare the costs of issuing Series administrative costs of issuing, servicing, and redeeming savings bonds, EE and Series I savings bonds with relative to the marketable securities. those of issuing marketable Treasury securities. GAO was The cost-effectiveness of the savings bond program depends on whether asked to review this model to judge Treasury’s savings—in terms of the generally lower interest payments on its reliability in measuring the relative costs of Treasury’s savings bonds relative to marketable Treasury securities—exceed the costs borrowing alternatives. that Treasury incurs with processing the paper savings bond certificates. The question is complicated by the fact that the interest savings occur over the life of a savings bond, and that Treasury pays costs upfront at issuance and in the future when the savings bond is redeemed. GAO is recommending that the Bureau of the Public Debt revise As prescribed by the Office of Management and Budget and common the cost-effectiveness model so financial practice, in dealing with savings or costs over time, the value of that it provides reliable information future savings or costs must be discounted to present value. Treasury has on the costs of the savings bond program. As part of that revision, reported that its cost-effectiveness model does calculate the present values the bureau should consider of the relative costs of savings bonds and marketable Treasury securities. updating some of the key data on However, because of flaws in the design and implementation of the the performance of the savings spreadsheet used to calculate these present values, the cost-effectiveness bond program, particularly on model’s results do not provide the Bureau of the Public Debt, Treasury, or savings bond redemption patterns. Congress with accurate information that is needed to assess the relative costs of issuing debt through savings bonds or marketable Treasury securities, or to manage the savings bond program. Further, the bureau has not updated some key data elements in the cost-effectiveness model. In particular, citing budget considerations, the bureau uses data on the redemption patterns for savings bonds that date back to 1993, which do not reflect the effects of the wide variety of financial instruments now available to investors. www.gao.gov/cgi-bin/getrpt?GAO-03-513. To view the full report, including the scope and methodology, click on the link above. For more information, contact Thomas J. McCool at (202) 512-8678 or McCoolT@gao.gov. Contents Letter 1 Results in Brief 2 Background 3 Conceptual Design for Estimating Savings Bond Cost-effectiveness Is Appropriate, but Model Calculations Contain Errors 8 Key Model Parameters and Components May Not Be Reliable 15 Conclusions 20 Recommendations 21 Agency Comments and Our Evaluation 22 Appendixes Appendix I: Objectives, Scope, and Methodology 26 Appendix II: Present Value Theory and Model Calculations 27 Appendix III: Future Value Examples for Series EE and Series I Savings Bonds for Bonds 5 Years and Older 30 Appendix IV: Model Calculations Detail 32 Appendix V: Comments from the Bureau of the Public Debt 35 GAO Comments 43 Appendix VI: GAO Contacts and Staff Acknowledgments 44 GAO Contacts 44 Acknowledgments 44 Tables Table 1: Savings Bonds and Selected Treasury Securities 4 Table 2: Key Parameters of the Savings Bond Cost-effectiveness Model 7 Table 3: Redemption Value Calculation for Series EE and Series I Savings Bonds 5 Years and Older 12 Table 4: BPD Changes to Savings Bond Cost-effectiveness Model Parameters since 1995 16 Figure Figure 1: Conceptual Design of the Savings Bond Cost-effectiveness Model 9 Page i GAO-03-513 Savings Bonds Contents Abbreviations BPD Bureau of the Public Debt CMT constant maturity Treasury FV future value OMB Office of Management and Budget PV present value This is a work of the U.S. Government and is not subject to copyright protection in the United States. It may be reproduced and distributed in its entirety without further permission from GAO. It may contain copyrighted graphics, images or other materials. Permission from the copyright holder may be necessary should you wish to reproduce copyrighted materials separately from GAO’s product. Page ii GAO-03-513 Savings Bonds A United States General Accounting Office Washington, D.C. 20548 June 16, 2003 Lert The Honorable Ernest J. Istook, Jr. Chairman, Subcommittee on Transportation, Treasury, and Independent Agencies Committee on Appropriations House of Representatives Dear Mr. Chairman: Savings bonds, which offer low-risk, affordable investment opportunities to many Americans, represent almost 3 percent of the total Department of the Treasury (Treasury) securities outstanding but nearly 6 percent of the total nonmarketable Treasury securities outstanding.1 While savings bonds generally pay lower interest rates than marketable Treasury securities, Treasury incurs higher administrative costs to produce, market, service, and redeem savings bond certificates. Concerns have been raised regarding whether, and to what extent, savings bonds are cost effective for Treasury—whether Treasury’s administrative and tax deferral costs on savings bonds are more than offset by lower interest payments. To address these concerns, in 1985, Treasury introduced the savings bond cost- effectiveness model that measures, according to model documentation, the difference between the projected costs for raising funds through the issuance of $1 billion of new savings bonds and the estimated costs for comparable borrowing through marketable securities. In 1995, Treasury’s Bureau of the Public Debt (BPD) assumed responsibility for the model. BPD believes the model shows that over time savings bonds are a more cost-effective means of raising funds in that the administrative and tax deferral costs of issuing savings bonds are offset by the lower interest payments on savings bonds. This report responds to your July 16, 2002, request that we assess the effectiveness of BPD’s cost-effectiveness model. As agreed with your staff, this report presents our assessment of (1) the appropriateness of the model’s design to compare the costs associated with savings bonds with those of other Treasury debt and (2) the reliability of certain key parameters and components of the model. 1 Treasury Department, Bureau of the Public Debt, Monthly Statement of the Public Debt of the United States (April 30, 2003). Available from www.publicdebt.treas.gov. Page 1 GAO-03-513 Savings Bonds To address these objectives, we reviewed an electronic copy of the model, related hard-copy documentation, and savings bond program regulations. We did not assess the overall savings bond program or the accuracy or completeness of all data used in the model. As a result, we do not know what effect such data had on the model’s cost-effectiveness calculation. Appendix I contains a more detailed description of our scope and methodology. We conducted our work in Washington, D.C., from September 2002 through April 2003 in accordance with generally accepted government auditing standards. Results in Brief Treasury has presented the savings bond cost-effectiveness model as a way to measure the cost-effectiveness of savings bonds over time, one that is based on a present value approach—calculating the value today of future costs and revenues in order to provide a common basis for comparison between savings bonds and marketable Treasury securities. The conceptual design underlying the savings bond cost-effectiveness model reflects Office of Management and Budget (OMB) guidance and common financial economics practice. According to OMB Circular A-94, such analysis is appropriate when the benefits of competing alternatives— alternative debt instruments in this case that provide equal funds to Treasury—are the same. A program is cost effective if, on the basis of appropriately measuring the costs of competing alternatives over time, it has the lowest costs, expressed in present value terms, for a given amount of benefits. For savings bonds, the question is whether, over time, savings bonds cost less than marketable Treasury securities. However, the model as constructed does not provide Treasury with the information it needs to determine whether savings bonds are cost effective because of errors in several steps in the model. In particular, we found that the model does not accurately calculate the present value of either alternative and thus does not provide a valid comparison. BPD has changed several parameters in the model in an effort to better reflect changes in the savings bond program. However, despite these enhancements, some of the data used to adjust the model’s parameters have not been updated and do not incorporate historical experience. In particular, data on savings bond redemptions do not reflect the most recent experience, possibly affecting the validity of the model’s cost-effectiveness estimates. In addition, the model contains other inaccuracies that could affect its reliability and accuracy. Finally, the model has not been subject to Page 2 GAO-03-513 Savings Bonds ongoing and periodic reviews by independent external reviewers, a common practice endorsed by OMB. This report includes recommendations to the Secretary of the Treasury that are designed to increase the reliability of the savings bond cost- effectiveness model. We obtained comments on a draft of this report from BPD. BPD disagreed with our description of the savings bond cost- effectiveness model and our conclusion that the model’s comparisons were invalid, but agreed in general with our recommendations. However, BPD noted that the goal of moving to an electronic environment for savings bonds would make it appropriate to “shelve” the current model. BPD’s comments are discussed in the Agency Comments and Our Evaluation section, and its written comments are reprinted in appendix V. Background Savings bonds offer investors the ability to purchase securities with lower minimum denominations than those for marketable Treasury securities. In response to concerns raised regarding the cost-effectiveness of the savings bond program as a funding mechanism for federal government operations, Treasury created a cost-effectiveness model that is now used and maintained by BPD. The model was intended to compare the projected costs for $1 billion of new savings bond borrowing and comparable borrowing through marketable Treasury securities. The model is based on the characteristics of the Series EE and Series I savings bonds and is intended to compare these costs on a present value basis. Savings Bond Program Treasury is authorized to borrow money on the credit of the United States to fund federal government operations. Within Treasury, BPD is responsible for prescribing the debt instruments, limiting and restricting the amount and composition of the debt, paying interest to investors, and accounting for the resulting debt. However, Treasury sets the financial terms and conditions of savings bonds and marketable Treasury securities, including denomination and pricing changes.2 2 Treasury securities are marketable bills, notes, and bonds issued at various schedules throughout the year. These instruments are negotiable debt obligations of the U.S. government secured by its full faith and credit. Treasury bills are short-term obligations issued with a term of 1 year or less. Treasury notes have a term of more than 1 year, but not more than 10 years. Treasury bonds are long-term obligations issued with a term of more than 10 years. Page 3 GAO-03-513 Savings Bonds Savings bonds are an alternative for investors unable or unwilling to pay the minimum denomination of marketable Treasury securities. Table 1 describes several principal differences between Series EE and Series I savings bonds and selected marketable Treasury securities. Table 1: Savings Bonds and Selected Treasury Securities Savings bonds Marketable Treasury securities Series EE Series I Fixed-principal notes Inflation-indexed notesa General Nonmarketable. Sold at 50 Nonmarketable. Sold at face Marketable. Sold at auction Marketable. Sold at auction features percent of face value in value in denominations as low with a minimum face value with a minimum face value denominations as low as as $50. of $1,000. of $1,000. $50. Interest rate Calculated as 90 percent Calculated to provide a fixed Rate is determined at Rate is determined at of 6-month averages of 5- rate plus a semiannual auction. auction. The fixed rate of year Treasury securities inflation adjustment. interest is applied to the yields. inflation-adjusted principal. Earnings Interest is paid when the Interest is paid when the bond Interest is paid Interest is paid semiannually bond is redeemed; value is redeemed; generally semiannually. (Interest based on the inflation- increases monthly with increases in value monthly, payment is commonly called adjusted principal value of accrued interest. but may remain unchanged in the note’s “coupon”). the note; in the event of times of deflation. deflation, interest payments will decrease. Earn interest for up to 30 Earn interest for up to 30 Interest paid until the note Interest paid until the note years. years. matures; more than 1 year matures; more than 1 year but not more than 10 years. but not more than 10 years. Redemption Can be redeemed after Can be redeemed after first Marketable, can be sold at Marketable, can be sold at and cashing first 12 months.b A 3- 12 months. A 3-month interest any time prior to maturity any time prior to maturity options month interest penalty penalty applies to bonds date. date. applies to bonds redeemed during the first 5 redeemed during the first years. 5 years. Page 4 GAO-03-513 Savings Bonds (Continued From Previous Page) Savings bonds Marketable Treasury securities Series EE Series I Fixed-principal notes Inflation-indexed notesa Special federal Federal income tax on Federal income tax on Interest income is subject to Interest income is subject to tax treatment earnings may be deferred earnings may be deferred until federal income tax, which is federal income tax, which is until redemption; all or redemption; all or part of generally reported in the generally reported in the part of earnings may be earnings may be excluded year paid. year paid. Inflation excluded from federal from federal income tax if adjustments must be income tax if used for used for qualified education reported in the year earned. qualified education expenses. expenses. Sources: BPD and the Internal Revenue Service. Note: Table data taken from the following publications of the Treasury Department, Bureau of the Public Debt: FAQs Regarding Treasury Bills, Notes, and Bonds, The U.S. Savings Bonds Owner’s Manual (June 2002), Minimum Holding Period For Savings Bonds Extended to 12 Months (press release: January 15, 2003), available from www.publicdebt.treas.gov; and Internal Revenue Service, Investment Income and Expenses for 2002 Returns, Publication 550, available from www.irs.gov. a Treasury notes and bonds for which the interest and redemption payments are tied to inflation. Treasury bills are not offered in inflation indexed form. b The 12-month period, referred to as the minimum holding period, is the length of time from the issue date that a bond must be held before it is eligible for redemption. On January 15, 2003, Treasury announced that the minimum holding period that applies to U.S. Savings Bonds would be extended from 6 to 12 months, effective for bonds issued on and after February 1, 2003. Series EE and Series I savings bonds bearing issue dates prior to February 2003 retain the 6-month minimum holding period in effect when they were issued. In March 2002 the Treasury Assistant Secretary for Financial Markets testified before the House Appropriations Committee, Subcommittee on Treasury, Postal Service, and General Government that Treasury believes that the availability of a savings vehicle with the full faith and credit of the United States should not be limited to those who can afford the minimum $1,000 denominations available in auctions of marketable Treasury securities. The official also said that even though savings bonds are not the most efficient form of borrowing in operational terms, Treasury would continue to offer them to the public.3 3 In March 2002, the Commissioner of the Public Debt testified before the Subcommittee on Treasury, Postal Service, and General Government, House Committee on Appropriations that savings bonds are the only security sold to the public in the form of paper certificates. Page 5 GAO-03-513 Savings Bonds Treasury is seeking to reduce the operational costs of savings bonds by offering the securities in paperless form. Treasury has started to offer savings bonds that are held in direct Treasury accounts instead of issuing paper certificates for the bonds. The Series EE and Series I savings bonds are available through the new TreasuryDirect system.4 A BPD planning document describes BPD’s objective as enabling Treasury to stop issuing paper savings bonds and thus begin to realize the long-term cost reductions expected from additional automation and more efficient processing. Savings Bond Cost- In response to concerns raised regarding the cost-effectiveness of the effectiveness Model savings bond program as a funding mechanism for federal government operations, Treasury created a cost-effectiveness model. According to a Treasury report to the House Committee on Appropriations and Committee on Financial Services, the savings bond cost-effectiveness model has been used to assess potential changes in the financial terms and conditions for Series EE and Series I savings bonds.5 According to model documentation, BPD also uses model results to project and trace annual costs and recoveries for distinct cost centers over the life of a savings bond loan. What is collectively referred to as the savings bond cost-effectiveness model comprises two submodels, Series EE and Series I, with the differences between the two reflecting differences between the two series of savings bonds. The results of each submodel are averaged to estimate the overall cost-effectiveness of the savings bond program. According to a BPD official, the model calculates the value of a single savings bond and its costs to Treasury, and extends this to the total savings bond population in a given year. Subsequently, the model attempts to quantify the differences between the savings bonds and marketable Treasury securities (noted in table 1).6 4 The original TreasuryDirect system was a Web-based system for marketable Treasury securities that is now called Electronic Services for Treasury Bills, Notes, and Bonds. The new TreasuryDirect is a Web-based system that allows investors to establish accounts to purchase, hold, and conduct transactions for Series EE and Series I savings bonds on-line. 5 Department of the Treasury, Report to the Committee on Appropriations and the Committee on Financial Services, United States House of Representatives: On Federal Debt Financing and the Role of United States Savings Bonds (Washington, D.C.: July 1, 2002). 6 Treasury has not issued bonds of any maturity since its decision in October 2001 to suspend issuance of the 30-year bond. Page 6 GAO-03-513 Savings Bonds The model was intended to compare the projected costs for $1 billion of new savings bond borrowing and those for $1 billion in marketable Treasury securities on a present value basis, that is, discounting the costs over time to permit a valid comparison. The savings bond cost- effectiveness model utilizes seven key parameters: administrative costs, historic redemption patterns, sales volume, savings bond yields, maturity period, equivalent marketable yield, and tax recovery. Table 2 describes the key parameters of the model in detail. Table 2: Key Parameters of the Savings Bond Cost-effectiveness Model Key parameters Description Administrative costs Includes all federal government costs for marketing/issuing, servicing, and redeeming savings bonds.a Issue cost comprises marketing/issuing costs plus one-half of servicing costs. Redemption cost comprises cost of redemption plus one-half of servicing costs. Each of these total costs is then divided by its respective transactions during the prior fiscal year budget activity to return unit cost to issue per bond and unit cost to redeem per bond. Unit costs per bond are the same across all denominations. Historic redemption A probability distribution of the number of bonds redeemed by patterns denomination and period outstanding. The data were derived from the redemption patterns from 1957 through 1993. Monthly rates of redemption in the first 3 years outstanding are expressed as the quotient of the total bonds redeemed at a given age by the total bonds of that age outstanding. Annual rates of redemption for bonds that remain outstanding for 3 years or longer were similarly derived. The annual rates are prorated to allocate bond redemptions equally among the 12 months in a year. The model applies the redemption probabilities of Series EE bonds to similarly priced Series I bonds (that is, the probabilities for a $100 Series EE bond and a $50 Series I bond are equal). Sales volume The number of bonds issued by denomination in the prior fiscal year. Savings bond yields Series EE – 90 percent of 6-month averages of 5-year Treasury securities yields. Series I - a fixed rate of return and a semiannual inflation rate. Maturity period Series EE and Series I bonds earn interest for 30 years. The model incorporates an additional 20 years of redemption patterns beyond final maturity. Page 7 GAO-03-513 Savings Bonds (Continued From Previous Page) Key parameters Description Equivalent marketable An estimate of the comparable borrowing costs for marketable yield Treasury securities based on the constant maturity yield curve. Tax recovery An estimate of taxes paid by an investor upon redeeming the bond. b Source: BPD model documentation. a According to model documentation, since BPD’s administrative costs for marketable Treasury securities are negligible to the total amount financed, they are not built into the model. b The tax recovery rate is provided by Treasury’s Office of Tax Policy, which, among other functions, provides the official estimates of all government receipts for Treasury cash management decisions. Conceptual Design for OMB guidelines state that a cost-effectiveness analysis is appropriate to use in an analysis of government programs when the benefits of competing Estimating Savings alternatives are the same or where a policy decision has been made that the Bond Cost- benefits of a program must be provided.7 A program is cost effective if, on the basis of life cycle cost analysis of competing alternatives, it is effectiveness Is determined to have the lowest costs expressed in present value terms for a Appropriate, but Model given amount of benefits.8 The conceptual design underlying the savings Calculations Contain bond cost-effectiveness model reflects this OMB guidance. However, the present value calculations in the model contain errors. As a result, the Errors model’s estimated “present values” do not follow OMB guidance and common financial economics practice, and the model does not provide Treasury with the information it needs to determine whether savings bonds are cost-effective. Model’s Conceptual Design The model’s conceptual design follows OMB guidelines for cost- Follows OMB Guidelines effectiveness analysis. Figure 1 shows the conceptual design of the model. 7 Office of Management and Budget, Guidelines and Discount Rates for Benefit-Cost Analysis of Federal Programs, Circular A-94 (Washington, D.C.: October 29, 1992). This circular provides general guidance for conducting benefit-cost and cost-effectiveness analyses and serves as a checklist of whether an agency has considered and properly dealt with all the elements for sound benefit-cost and cost-effectiveness analyses. 8 OMB states that life cycle cost represents the overall estimated cost for a particular program alternative over the time period corresponding to the life of the program, including direct and indirect initial costs plus any periodic or continuing costs of operation and maintenance. Page 8 GAO-03-513 Savings Bonds Figure 1: Conceptual Design of the Savings Bond Cost-effectiveness Model OMB Circular A-94, which is applicable to executive branch agencies, provides that the standard criterion for deciding whether a government program is cost-effective is net present value—a comparison of the discounted monetized value of the expected life cycle costs of alternative means of achieving the same stream of benefits. However, in its comments on this report BPD asserted that the model’s approach follows an alternative OMB method to determine cost-effectiveness. BPD stated that the model measures cost-effectiveness as the “relative financial benefit from two borrowing options whose overall costs are identical. Treasury’s benefit from each alternative is the amount of financing realized at the time Page 9 GAO-03-513 Savings Bonds borrowing occurs.” We have addressed this comment in the Agency Comments and Our Evaluation section. A key concept in finance is recognizing that the value associated with funds received or paid at different points changes over time. Funds have a time value because of the opportunity to invest them at different interest rates and in different financial alternatives. Investors demand some compensation for making funds available today in return for future repayment. For example, the interest paid on a loan is a measure of this compensation. Essentially, a present value calculation measures the value today that would be equivalent to a future payment, or stream of payments, by discounting the future payments (using an appropriate discount rate).9 For Treasury, this is the value today of the future payments to investors of securities offered for sale which, in the context of the model, is the redemption value of Series EE and Series I savings bonds and the repayment stream of the alternative marketable Treasury security (that is, any coupons plus maturity value). Calculating the present value for each alternative takes the monetary value of costs over time and discounts them at an appropriate discount rate. Discounting transforms costs occurring in different time periods to a common unit of measurement (app. II describes this in greater detail). As table 1 notes, there are several distinctions between savings bonds and marketable Treasury securities; several of these are relevant to the model. Most notably, the interest rates and the timing of the interest payments are different. Accurate implementation of the conceptual design requires that the model address these issues in order to construct comparable present values for the costs of savings bonds and marketable Treasury securities. The model attempts to address these distinctions by (1) creating an after- tax present value discount factor for the marketable Treasury security from a 6-month average of the constant maturity yield curve, commonly referred to as the “constant maturity Treasury,” or CMT),10 and (2) reducing the 9 The interest rate used in calculating the present value of expected future benefits and costs. 10 The Federal Reserve Bank of New York collects prices for all actively traded U.S. Treasury securities. Treasury takes this information and calculates a yield curve. The curve is known as the constant maturity yield curve because it gives an estimate of the yield on Treasury securities at the maturities shown even if no current Treasury security has a remaining maturity exactly equal to one of those points. Page 10 GAO-03-513 Savings Bonds present value of the marketable Treasury security by subtracting its estimated (that is, not paid) “discounted” coupons. Model Creates Cost- In general, the model is conceptually designed to create a marketable effectiveness Ratio Based Treasury security comparable to a savings bond such that the repayment stream (that is, any coupons plus maturity value) to an investor is equal to on Calculated “Present that of a savings bond’s net cost to Treasury (that is, redemption value Values” for Both adjusted for administrative unit costs and tax revenue implications). The Alternatives repayment stream of the created marketable Treasury security and the adjusted redemption value of the savings bonds represent costs to Treasury from offering these securities for sale. From this point, the model is intended to compare the costs of these two financing alternatives on a present value basis. According to model documentation, the present value of the marketable Treasury security is constructed by discounting the savings bond’s redemption value, adjusted for Treasury’s unit cost of redemption and tax revenue implications, at an equivalent after-tax rate for marketable Treasury securities of the same maturity.11 The model’s calculation of the redemption value of the Series EE and Series I savings bond is similar; changes are due to the different structures of the two series. Table 3 provides additional detail on the redemption value calculation and variables for both the Series EE and Series I savings bond. Appendix III provides examples of redemption value calculations for both the Series EE and Series I savings bond. 11 According to model documentation, the model assumes that the tax recovery for the marketable Treasury security occurs simultaneously with each interest payment. Page 11 GAO-03-513 Savings Bonds Table 3: Redemption Value Calculation for Series EE and Series I Savings Bonds 5 Years and Older Series EE, FV = PV * {[1+(i/2)](m/6)}, where Series I, FV = PV * {[1+(CR/2)](m/6)}, where FV (future value) = redemption value on FV (future value) = redemption value on redemption (accrual) date rounded to the redemption (accrual) date rounded to the nearest cent nearest cent PV (present value) = redemption value at PV (present value) = redemption value at the beginning of the semiannual rate period the beginning of the semiannual rate period i = savings bond rate CR (composite rate) = fixed rate of return m = number of full calendar months elapsed plus the semiannual inflation rate during the semiannual rate period m = number of full calendar months elapsed during the semiannual rate period Sources: Series EE: 31C.F.R. § 351.2-(k)(4)(ii)(A); Series I: 31C.F.R. § 359.2-(e)(4)(ii)(A). Note: Bonds are subject to a 12-month holding period and those redeemed before 5 years are subject to a 3-month interest penalty. All calculations of interest are based on a hypothetical savings bond with a denomination of $25. The tax revenue implications are reflected in the model as a tax recovery rate. The model assumes that all savings bond tax recoveries are deferred until redemption.12 Tax recovery—the taxes collected on savings bond earnings that had been deferred until redemption—increases the revenues to Treasury. The model calculates the effect of tax recovery, in terms of life cycle costs for the model, by reducing the amount Treasury pays to an investor at redemption. However, the tax recovery rate is reduced in the model to reflect the education bond program. In general, as shown in table 1, savings bonds are eligible for tax benefits upon redemption when used for qualified education expenses. 12 An investor may choose to use the accrual method of accounting, where increases in the redemption value are reported as interest each year, or the cash method of accounting, where reporting of interest earned is postponed until the earlier of the year in which the bond is cashed or disposed of or the year in which the bond matures. Page 12 GAO-03-513 Savings Bonds The administrative unit cost to Treasury from redeeming savings bonds reduces the revenues to Treasury. The model calculates the effect of administrative unit redemption cost, in terms of life cycle costs for the model, by increasing the amount Treasury pays to an investor at redemption. The model constructs an after-tax “discount factor” based on a 6-month average of the CMT.13 At the time of our review, the window was the 6-month period ending October 31, 2001. According to BPD officials, the model is intended to perform an additional step to calculate the “present value” of the marketable Treasury security. This additional step, according to model documentation, is intended to reflect the difference between savings bonds, which do not pay periodic interest, and marketable Treasury securities that do pay such interest in the form of coupons. The model treats the coupon payments that the marketable Treasury security would pay as a separate security in which the tax recovery is simultaneous with the payment. First, the estimated coupons are created based on the savings bond’s redemption value, adjusted for Treasury’s unit cost of redemption and tax revenue estimates. Second, these coupons are “discounted” by an after-tax “discount factor” based on a 6-month average of the CMT. BPD believes that these coupons would reduce the benefit of the initial marketable Treasury security and therefore its “present value.” According to model documentation, these are subtracted from the “discounted” savings bond final payout, adjusted for Treasury’s unit cost of redemption and tax revenue implications. The model calculations for the “present value” of the marketable Treasury security, however, do not follow model documentation in that the savings bond final payout is not discounted. BPD officials confirmed that the model calculations actually construct the “present value” of the marketable Treasury security as equal to the redemption value of the savings bond, adjusted for Treasury’s unit cost of redemption and tax revenue implications, net of estimated “discounted” coupons. According to model documentation, the “present value” of the savings bond is its issue price less the unit cost to issue. The model’s calculation returns a value that is equal to Treasury receipts from a savings bond, net of the administrative unit cost of issuance. 13 The tax rate applied to the 6-month average of the CMT is the unadjusted tax recovery rate provided by Treasury’s Office of Tax Policy. Page 13 GAO-03-513 Savings Bonds As previously mentioned, the model is intended to compare a savings bond and a marketable Treasury security on a present value basis. The difference, according to a BPD official, is then translated to the total savings bond population in a given year and converted to a ratio of millions of dollars in cost per $1 billion borrowed. The model calculation takes the difference between the two “present values” described above, projects the difference across the sales volume for the prior fiscal year, and then converts the difference to a ratio that measures cost savings in millions per $1 billion borrowed. Appendix IV provides a more detailed discussion of the model calculations. BPD’s Definition of Present Although Treasury has presented the model as measuring cost- Value Does Not Follow OMB effectiveness on a present value basis, most notably in a July 2002 report to Congress, the model does not construct a present value comparison in Guidance accordance with OMB guidance. Our review indicates that the model does not accurately incorporate all the life cycle costs in the present value calculations for either alternative, does not calculate and apply a true economic discount factor needed to derive present value that would be relevant to the time periods, and ultimately compares values that are not equivalent based on the time value of money. The result is that the model’s calculation of a cost-effectiveness ratio does not provide an accurate present value assessment of the alternatives. As previously discussed, to create comparable borrowing between the two alternatives, the model is intended to set the repayment stream (that is, any coupons plus maturity value) of the marketable Treasury security equal to that of a savings bond’s net cost to Treasury (that is, redemption value adjusted for administrative unit costs and tax revenue implications). However, the model calculation does not incorporate all the life cycle costs of the savings bond into the marketable Treasury security’s “present value” calculation — the initial administrative cost of issuing the savings bond (that is, unit cost to issue) is not included. In addition, the model calculation does not incorporate all the life cycle costs of the savings bond into the saving bond’s “present value” calculation — the redemption value paid to an investor and the final administrative cost of the savings bond (that is, unit cost to redeem) is not included. The present value of a bond (or bond price) is equal to the present value of its expected cash flows (that is, any coupons plus maturity value). As noted previously, BPD officials confirmed that the model measures what it terms the “present value” of the marketable Treasury security as equal to the Page 14 GAO-03-513 Savings Bonds redemption value of the savings bond, adjusted for Treasury’s unit cost of redemption and tax revenue implications, net of estimated “discounted” coupons. However, this calculation implicitly values current and future funds as the same. In addition, as previously discussed, the model treats coupons as if they reduce the benefit of the marketable Treasury security and therefore its “present value.” However, since the CMT already reflects the value of the coupons that Treasury is obligated to pay, reducing the benefit to Treasury essentially counts the coupons twice. Additionally, the construction of the discount factor in the model departs from OMB guidance since the model’s “discount factor” does not create an appropriate time value. Further, the model treats Treasury receipts from a savings bond, net of the administrative unit cost of issuance, as the “present value” of the savings bond. However, the model does not include or discount over time the savings bond’s redemption value in this calculation, and therefore the model does not reflect a time value associated with these funds, or present value as the term is used in OMB guidance or in general finance usage. Key Model Parameters The savings bond cost-effectiveness model utilizes seven key parameters: administrative costs, historic redemption patterns, sales volume, savings and Components May bond yields, maturity period, equivalent marketable yield, and tax recovery. Not Be Reliable Since 1995, when BPD assumed responsibility for the model, it has made four model enhancements in an effort to better reflect changes in the savings bond program, three of which directly affect these parameters.14 Table 4 presents BPD’s changes to the three key model parameters since 1995. However, despite these enhancements, some of the data used to adjust the model’s parameters have not been updated and do not incorporate historical experience. In addition, the model contains other inaccuracies that could affect its reliability and accuracy. Finally, the model has not been subject to ongoing and periodic reviews by independent external reviewers, a common practice endorsed by OMB. 14 The fourth change, building cost centers, does not directly affect the model parameters. Page 15 GAO-03-513 Savings Bonds Table 4: BPD Changes to Savings Bond Cost-effectiveness Model Parameters since 1995 Parameters BPD changes Redemption The model originally based bond redemption projections on probabilities current snapshots of redemption activity. To limit the model’s exposure to short-term market swings, BPD developed redemption patterns based on longer-term historical data (1957-93). Activity beyond Series EE and Series I bonds earn interest for 30 years. maturity However, not all bonds are redeemed before or at this final maturity; some owners choose to hold them even though they are no longer earning interest. For this reason, BPD refined the model to incorporate redemption patterns for 20 years beyond final maturity. Tax recovery Savings bonds have an education bond feature that is a tax benefit to investors; participation does not occur until investors actually redeem their bonds. According to BPD, while the full effects of the program are not known, BPD estimates the program’s effect in the model by reducing savings bond tax recovery by 10 percent, an estimate it believes to be at or above the maximum reduction in tax recovery. Source: BPD model documentation. Despite Enhancements, The first enhancement affects a key calculation in the savings bond cost- Model Results May Not Be effectiveness model: the redemption value, or future value, of the savings bond over time. These values form the basis for constructing a marketable Accurate Treasury security that is the alternative to savings bonds. The earlier bonds are redeemed, the less administrative costs are offset. Therefore, the accuracy of the model’s cost-effectiveness calculation depends heavily on the accuracy of predicted early redemptions. The key driver for the redemption values in the model is probability of redemption. The model accounts for redemption probabilities differently than in the original model transferred to BPD in 1995. According to BPD officials, the original model estimated redemption probabilities with the most recent 13 months of Series EE redemption data. When BPD assumed responsibility for the model, staff began estimating redemption probabilities for each denomination of Series EE savings bonds back to 1957. The current model continues to incorporate the historical redemption patterns from 1957 to 1993. However, citing cost concerns, BPD has not updated the probabilities to reflect redemption patterns of the most recent 10 years. Since then, however, a wide variety of financial instruments have Page 16 GAO-03-513 Savings Bonds become available to investors, which could affect the patterns of redemption. Further, the redemptions do not reflect current interest rates. As previously discussed, the model also applies the redemption probabilities of Series EE bonds to similarly priced Series I bonds (that is, the redemption probabilities for a $100 Series EE bond and a $50 Series I bond are equal). BPD has not estimated the redemption probabilities of Series I bonds, introduced in 1998, therefore the redemption probabilities applied in the Series I submodel have no direct relation to the Series I bond redemption patterns since 1998. The second model enhancement deals with the maturity period. The original model assumed the stated maturity date for both securities of 30 years. BPD adjusted the current model to include an additional 20-year horizon beyond the stated maturities of savings bonds and marketable Treasury securities to account for those investors who hold on to the securities past the maturity date. However, according to a statement made by Treasury, the regulations governing savings bonds provide that bonds for which no claims have been filed within 10 years of the maturity date will be presumed to have been properly paid. The 20-year horizon enhancement appears to be inconsistent with this Treasury statement. Further, adding the 20 years appears to be inconsistent with OMB guidance for the alternatives to be compared over their stated life cycles, which for both alternatives should be the 30-year maturity period. Finally, the third enhancement to the model adjusts the tax recovery rate for savings bonds by 10 percent to account for the education bond program. The 10 percent adjustment was an estimate since there was no program experience to guide the adjustment. The education bond benefit, which allows for the exclusion of interest earned subject to certain rules and limits, applies only to savings bonds. Adjusting the tax recovery rate for savings bonds to reflect this program is appropriate. However, the education bond program was introduced in 1990, providing program experience of at least 12 years. BPD has not analyzed whether the historical experience is consistent with the 10 percent adjustment and thus does not know whether the adjustment improves the model’s accuracy. Page 17 GAO-03-513 Savings Bonds Discontinuance of 30-Year A BPD official told us that the equivalent marketable yield, or CMT, has the Marketable Treasury Bonds strongest impact on model results. The CMT is the basis for BPD’s “discount factor” used to derive the “present value” of the alternative Directly Affects the marketable Treasury security. Treasury discontinued the issuance of the 30- Marketable Yield Model year Treasury bond in October 2001, however, directly affecting how the Parameter discount rate is calculated. Beginning on February 18, 2002, Treasury ceased publication of the 30-year constant maturity series. Instead, Treasury publishes a Long-Term Average Rate and a linear extrapolation factor that can be added to the Long-Term Average Rate to allow interested parties to compute an estimated 30-year rate.15 BPD staff told us that BPD is still considering how to reflect this change in the model’s “discount factor.” Other Model Features Could The model coding contains additional inaccuracies that, in comparison to Affect the Reliability of the present value inaccuracy, appear to have a minor impact. Also, the model’s use of older software and lack of controls over changes may allow Model Results additional errors to remain undetected. A coding error in the bonds redeemed calculation occurs in some denominations for both submodels. From the time of issuance through 4 months outstanding, the formula uses the probability of redemption for the month following the correct month. BPD staff told us this error occurred during model maintenance by BPD staff. Additionally, BPD staff told us that this error would be corrected (app. IV describes the correction for this calculation). Another inaccuracy involves the redemption value calculation in the Series I submodel. The calculation there does not match the savings bond regulations since the redemption value does not reflect the accrued value at the beginning of each semiannual period. 15 The Long-Term Average Rate is the arithmetic average of the bid yields on all outstanding fixed-coupon securities (i.e., excludes inflation-indexed securities) with 25 years or more remaining to maturity. This series first appeared on February 19, 2002, following discontinuation of the 30-year Treasury constant maturity series. Page 18 GAO-03-513 Savings Bonds In addition, the savings bond cost-effectiveness model is maintained in older software.16 Use of the older software can be appropriate, but does increase the difficulty in maintaining and updating the model without introducing errors. As noted above, BPD acknowledged one such error. BPD staff told us that they have not moved the model into current software because of concerns that the software’s features used to calculate the scenario effects of program changes will not function properly. During the course of our review, we also found that the model contained unlabeled and undocumented data fields. BPD staff told us that these fields were remnants of scenarios that staff had run on the model in the past, which were accidentally left in the model when it was sent to us for review. One aspect of an effective general control and application environment is the protection of data, files, and programs from unauthorized access, modification, and destruction. BPD staff could, by saving scenario data in the master model file, inadvertently add, alter, or delete sensitive data or coding. BPD Has Not Requested an While OMB guidance calls for an independent external review of cost- Independent External effectiveness models, as well as assessments of their accuracy and reliability, BPD has not commissioned such analysis. As a result, BPD Review of the Model cannot assess the accuracy and reliability of the model. OMB guidelines provide elements for a cost-effectiveness analysis and promote subjecting such analyses to independent external reviews. Verification and explicit assumptions are two of the four elements OMB identified for a cost-effectiveness analysis. OMB states that verification through retrospective studies to determine whether anticipated benefits and costs have been realized are potentially valuable. Such studies can be used to determine necessary corrections in existing programs, and to improve future estimates of benefits and costs in these programs. Agencies should have a plan for periodic, results-oriented evaluation of program effectiveness. OMB adds that a cost-effectiveness analysis should be explicit about the underlying assumptions used to arrive at estimates of future benefits and costs and include a statement of the assumptions, the rationale behind them, and a review of their strengths and weaknesses. Key 16 The model is maintained in version 5 of a spreadsheet program that is currently marketed in version 9. Page 19 GAO-03-513 Savings Bonds data and results should be reported to promote independent analysis and review. OMB guidance also acknowledges that estimates are typically uncertain because of imprecision in both underlying data and modeling assumptions and states that analyses should attempt to characterize the sources and nature of uncertainty. In analyzing uncertain data, objective estimates of probabilities, such as those derived from market data, should be used whenever possible. Any limitations of the analysis because of uncertainty or biases surrounding the data or assumptions should be discussed. In addition, major assumptions should be varied and net present value and other outcomes recomputed to determine how sensitive outcomes are to changes in the assumptions. In general, sensitivity analysis should be considered for estimates of benefits and costs, the discount rate, the general inflation rate, and distributional assumptions of probabilities. Models used in the analysis should be well documented and, where possible, available to facilitate independent review. BPD has not independently verified the cost-effectiveness model. According to BPD officials, a survey and investigations team from the House Committee on Appropriations, which visited BPD’s Parkersburg, West Virginia, location in 1996, conducted the only review of the savings bond cost-effectiveness model. Since the team did not initiate further inquiry, BPD officials said they assumed that the team had found no issues requiring further review and discussion. Although BPD and Treasury officials have maintained in congressional testimonies and in a recent report that the model results are accurate, to date neither BPD nor Treasury has requested an independent external review to validate the savings bond cost-effectiveness model. Further, while BPD has used the model to estimate the potential effects of changes in the savings bond program, it has not sought to conduct any sensitivity analysis that could reveal the model’s limitations. Conclusions Our review of BPD’s savings bond cost-effectiveness model indicates that the model’s results do not provide BPD, Treasury, OMB, or Congress appropriate information to assess the relative costs of the savings bond program versus marketable Treasury securities as a source of raising funds. Although the model was intended to compare savings bonds and marketable Treasury securities on a present value basis, the model’s comparison is not based on present values and thus does not follow OMB guidance and common financial economics practice. As previously Page 20 GAO-03-513 Savings Bonds discussed, a discount factor brings future costs and revenues into present value terms to permit comparisons. While the model calculates a value that BPD terms a “discount factor,” the calculation is incorrect and, as a result, the model does not correctly calculate the present value of the alternatives. In addition, this calculated value is not applied consistent with the model’s conceptual design and OMB guidance. Therefore the cost-effectiveness ratio that the model creates does not provide BPD with the information it needs to assess the relative costs of the savings bond program and marketable Treasury securities to determine which financing approach offers a greater financial benefit to Treasury. The model also uses data that may not be reliable. In particular, the probabilities of redemption for the Series EE bond are 10 years out of date and BPD has not estimated any probabilities of redemption that have any direct relation to the Series I bond redemption patterns since 1998 when these bonds were first introduced. The model also incorporates a time horizon that extends beyond the life cycles of either security and distorts the cost-effectiveness analysis, allowing a longer time period for the administrative costs of savings bonds to be offset. Finally, the reduction in the tax recovery rate to reflect the education bond program is not based on actual program experience and may be over- or underestimating the financial impact of the program to Treasury. Given that the model uses data that may not be reliable and BPD has not decided how to reflect the discontinuance of the 30-year constant maturity series in the model’s “discount factor,” we did not make corrections to the model. As a result, we do not know to what degree the present value errors and these data affect the model’s cost-effectiveness ratio. BPD’s ability to assess the impact of policy changes to the savings bond program, project cost centers for the savings bond program, and determine cost-effectiveness in relation to marketable Treasury securities is hampered by fundamental errors in the present value calculations. When combined with model data that may not be reliable, the need for independent reviews of cost-effectiveness and sensitivity analyses, which are called for in OMB Circular A-94, becomes particularly important. Recommendations Because of the importance of measuring the cost-effectiveness of financing mechanisms used to fund the operations of the federal government, we recommend that the Secretary of the Treasury direct that the Commissioner of the Public Debt in conjunction with Treasury’s Office of Page 21 GAO-03-513 Savings Bonds Domestic Finance revise the savings bond cost-effectiveness model to estimate the relative (or net) present value of the life cycle costs of issuing savings bonds versus marketable Treasury securities. As part of that revision, the Commissioner should do the following: • Update the Series EE probabilities of redemption to capture any changes in redemption patterns caused by the proliferation of financial products or interest rate changes in the last 10 years. At a minimum, Treasury and BPD should collect data for a sample of the more recent time period to test the validity of the 1957-93 data. • Base Series I bond redemption patterns on actual experience with those bonds. • Validate the cost estimate of education bond program participation based on the historical, 12-year data to date. • Replace the 30-year equivalent marketable rate. • Update the software used for the model to enhance BPD’s ability to maintain the model and protect against unauthorized modification. • Put in place a process for ongoing verification, sensitivity analysis, and independent external review of the model. Agency Comments and In a June 4, 2003, letter commenting on a draft of this report, the Commissioner of the Public Debt wrote that the cost-effectiveness model Our Evaluation conformed to OMB Circular A-94, sec. 5b, since it “measures Treasury’s relative financial benefit from two borrowing options whose overall costs are identical. Treasury’s benefit from each alternative is the amount of financing realized at the time borrowing occurs.” Noting that the model “is not intended to be a classic present value exercise,” the Commissioner explained that the model “compares the present value of a projected stream of payments associated with the sale of savings bonds with the amount realized from the sale.” BPD suspects it may have inadvertently misused the terms “discount factor” and “present value” in internal Treasury discussions. Further, BPD said that we did not understand the model’s life-cycle duration, the minimum holding period, and the Series I redemption values. Page 22 GAO-03-513 Savings Bonds The Commissioner noted that while BPD disagreed with our conclusion that the model’s comparisons were invalid, BPD generally agreed with our recommendations for updating the model. However, the Commissioner also noted that, with Treasury’s goal of moving toward a totally electronic environment for the savings bond program, “we think it's appropriate for us to shelve the existing model, which is based on paper bonds, and focus our attention on the transition to a fully electronic program.” We disagree with the Commissioner’s portrayal of the cost-effectiveness model as measuring “…Treasury’s relative financial benefit from two borrowing options whose overall costs are identical.” Neither the model documentation nor BPD’s public statements are consistent with this explanation. BPD’s model documentation explained that the savings bond cost-effectiveness model compares the projected costs for $1 billion of new savings bond borrowing and those for $1 billion in marketable Treasury securities on a present value basis. In March 2002 testimony before the House Appropriations Subcommittee on Treasury, Postal Service, and General Government, the Commissioner described the model as one that “…measures the cost-effectiveness of savings bonds vis-à-vis borrowing equivalent amounts of money with marketable issues. …Our latest calculations indicate that every $1 billion borrowed through Series EE and Series I savings bonds is $35 million less expensive than borrowing with marketable securities.” Additionally, the July 2002 report to the House Committees on Appropriations and Financial Services explained the savings bond cost-effectiveness model as one based on a present value analysis: The model compares the amount of funds raised by selling a given amount of Series EE and I bonds in various denominations and the present value of the future costs to Treasury in connection with issuing the bonds. If the amount raised is greater than the present value of the future costs associated with the bonds, taking into account administrative costs and tax benefits, then the program is deemed to be cost-effective. While we agree that an approach comparing the benefits of two approaches having identical costs would be a valid alternative to the present value approach that we described in our report, the model’s calculations do not support this analysis. Marketable Treasury securities and savings bonds can be compared by either comparing the costs of raising identical sums using two alternative debt instruments or by comparing the funds raised when the costs of the two instruments are identical. However, if BPD were to base the cost-effectiveness model on a comparison of the “financial benefit from two borrowing options whose overall costs are identical,” the key issue that this approach would have to address is that marketable Page 23 GAO-03-513 Savings Bonds Treasury securities and savings bonds do not necessarily have identical overall costs. The challenge of this modeling approach would be to appropriately measure costs over time of the two options in a way that would permit treating the costs as identical. Since the costs vary over time, accurately calculating the present value of the costs of the two options would be an essential step. However, we did not find, for reasons noted in the report, that the model accurately or reliably calculates the present value of the stream of costs associated with the sale of savings bonds. In particular, the report explains that the discount rate used to calculate the present value of the projected stream of costs is inappropriate. We have changed the report to recognize that BPD allocates a small number of redemptions prior to 6 months to reflect hardship waivers; these waivers are not discussed in BPD’s model documentation. We have not, however, changed the report in response to the Commissioner’s statements regarding life cycle costs and Series I redemption values. As the report notes, the 20-year extension on the life cycle appears to be inconsistent with regulations that provide that bonds for which no claims have been filed within 10 years of the maturity date are presumed to have been properly paid. Our analysis of the Series I savings bond redemption value found that the formula does not correctly recognize the savings bond’s accrued value at the beginning of each semiannual period. The Commissioner’s letter noted that BPD generally agrees with the recommendations for updating the model, but that BPD believes it appropriate to “shelve” the existing model and focus on the transition to a fully electronic retail securities program. We agree that the importance of many administrative costs will decline if BPD successfully transforms the current paper-based savings bond program to an electronic environment. Further, there may be changes in investors’ purchases and redemptions of savings bonds in an electronic environment. However, important differences will continue to exist between the costs of savings bonds and marketable Treasury securities, particularly the payment of coupons and the tax treatment of the two debt instruments. A model that accurately recognizes these differences will continue to be as crucial to understanding the relative cost-effectiveness of the two debt instruments as it is in the current paper-based environment. That model, furthermore, will have to be updated regularly to reflect the effect of any changes in investor preferences and behavior on the savings bond program Page 24 GAO-03-513 Savings Bonds as it moves into this new electronic environment. Our recommendations will remain appropriate for assessing the cost-effectiveness of the savings bond program managed in an electronic environment. As agreed with your office, unless you publicly announce its contents earlier, we plan no further distribution of this report until 30 days from its date. At that time, we will send copies to the Secretary of the Treasury, the Treasury Under Secretary for Domestic Finance, and the Commissioner of the Public Debt. Copies will be made available to others upon request. In addition, this report is also available at no charge on GAO’s Web site at http://www.gao.gov. If you have any further questions, please call me at (202) 512-8678 or mccoolt@gao.gov or James M. McDermott, Assistant Director, at (202) 512- 5373 or mcdermottjm@gao.gov. Sincerely yours, Thomas J. McCool Managing Director, Financial Markets and Community Investment Page 25 GAO-03-513 Savings Bonds Appendix I Objectives, Scope, and Methodology A A ppep nen d xIeis To assess the savings bond cost-effectiveness model, we obtained an electronic copy of the model as of fiscal year 2001 in addition to hard-copy background and supporting documentation. Given that the model is maintained in older software, Lotus 1-2-3 version 5, we reviewed the model using the same program and version to avoid corruption or translation errors. We then identified and reviewed the various regulations regarding the Series EE and Series I savings bond structure on which the cost- effectiveness model is based. In addition, we reviewed relevant portions of Internal Revenue Service publications regarding the tax implications of the savings bond program. We compared these information sources with the model coding to verify that the calculations reflect the structure of the savings bond program. To determine if the model constructed a present value comparison, we analyzed the model coding and supplied documentation to determine if (1) the model’s design matched Office of Management and Budget and conventional approaches and (2) the model’s calculations accurately implement the model’s design to arrive at a present value comparison. Given that the model calculations did not result in a present value comparison, we did not assess the accuracy or completeness of the data input used in the various model parameters and assumptions. As a result, we do not know what effect such data had on the model’s cost- effectiveness calculation. We conducted our work in Washington, D.C., from September 2002 through April 2003 in accordance with generally accepted government auditing standards. Page 26 GAO-03-513 Savings Bonds Appendix II Present Value Theory and Model Calculations AppenIx di The present value of a bond (or, bond price) is equal to the present value of its expected cash flows (any coupons plus maturity value). Each cash flow must be discounted at the relevant rate for the time period. t 0 1 2 3 ... n-1 n n+1 ... discount rate r0,1 r1,2 r2,3 ... rn-2,n-1 rn-1,n rn,n+1 ... cash flows coupon 0 C1 C2 C3 ... Cn-1 Cn 0 ... face 0 0 0 0 ... 0 M 0 ... Here, t represents time, where t = 0 represents the present moment, t = 1 represents the end of the first period, t = 2 represents the end of the second period, and so on. A given cash flow is specified to occur at the end of the given period. The discount rate, rs-1,s , is the appropriate one-period discount rate from s – 1 to s, at t = s (for s = 1, …, n).1 The appropriate one- period discount factor (or deflator) is as follows: 1 ---------------------------- ( 1 + r s – 1, s ) For example, to determine the value of C1 at t = 0, the appropriate discount rate is r0,1 and the appropriate one-period discount factor is as follows:2 1 C1 ----------------------- ; thus the present value at t = 0 of C1 received at t = 1 is: ---------------------- - ( 1 + r 0, 1 ) ( 1 + r 0, 1 ) For the cash flows specified in the above table, which are designed to mimic the cash flows of an n-period bond paying coupon Cs at t = s (for s = 1, …, n) and M at maturity, t = n, the present value at t = 0 is as follows: 1 In many explanations of present value, the discount rate is held constant, removing the need for rs-1,s to vary over time. 2 The factor that translates expected benefits or costs in any given future year into present value terms. Page 27 GAO-03-513 Savings Bonds Appendix II Present Value Theory and Model Calculations η Ct ---------------------------------------------- M - + --------------------------------------------- - , in which PV t = 0 (coupon + face) = Σ t=1 t η Π ( 1 + r s – 1, s ) Π ( 1 + r t – 1, t ) s=1 t=1 t Π ( 1 + r s – 1, s ) = ( 1 + r 0, 1 )* ( 1 + r 1, 2 )*...* ( 1 + r t – 1, t ) for some t >2, for example. s=1 Based on the above table, the following illustrations assume that the periods correspond to years (for example t = 1 represents the end of the first year). The present value of a one-period (that is 1-year) bond is as follows: C1 M PV = ----------------------- + ----------------------- ( 1 + r 0, 1 ) ( 1 + r 0, 1 ) The present value of a two-period bond is as follows: C1 C2 M PV = ----------------------- + ---------------------------------------------- + ---------------------------------------------- ( 1 + r 0, 1 ) ( 1 + r 0, 1 ) ( 1 + r 1, 2 ) ( 1 + r 0, 1 ) ( 1 + r 1, 2 ) Note that if r is identical through all time periods, such that r = r0,1 = r1,2 , the above two-time period present value is equivalent to the following: C1 C2 M PV = ---------------- + -----------------2- + -----------------2- (1 + r) (1 + r) (1 + r) The present value of a three-period bond is as follows: C1 C2 C3 M PV = ----------------------- + ---------------------------------------------- + --------------------------------------------------------------------- + --------------------------------------------------------------------- ( 1 + r 0, 1 ) ( 1 + r 0, 1 ) ( 1 + r 1, 2 ) ( 1 + r 0, 1 ) ( 1 + r 1, 2 ) ( 1 + r 2, 3 ) ( 1 + r 0, 1 ) ( 1 + r 1, 2 ) ( 1 + r 2, 3 ) In the illustrations above, the rate or rates used to discount each component is relevant to the time period. Page 28 GAO-03-513 Savings Bonds Appendix II Present Value Theory and Model Calculations Model Calculation for the “Present Value” of the Marketable Treasury Alternative Based on model documentation, the coupon payments are subtracted to reflect that the coupon payments on the Treasury alternative would reduce the benefit Treasury would receive from the initial security. Redemption Valuen substituted for M in the prior equation, where n = months outstanding Redemption Valuen * rn substituted for C in the prior equation, where n = months outstanding rn = Monthly after-tax “discount rate” (derived from CMT), where n = months outstanding The “present value” of a 1-month marketable alternative is calculated as follows: Redemption Value 1 *r 1 PV = Redemption Value 1 – ------------------------------------------------------- ( 1 + r1 ) However, the “present value” of a 2-month marketable alternative is calculated as follows: Redemption Value 2 * r 2 Redemption Value 2 * r 2 PV = Redemption Value 2 – -------------------------------------------------------- + -------------------------------------------------------- ( 1 + r2 ) ( 1 + r2 ) ( 1 + r1 ) Further, the “present value” of a 3-month marketable alternative is calculated as follows: Redemption Value 3 * r 3 Redemption Value 3 * r 3 Redemption Value 3 * r 3 PV = Redemption Value 3 – -------------------------------------------------------- + -------------------------------------------------------- + -------------------------------------------------------- ( 1 + r3 ) ( 1 + r3 ) ( 1 + r2 ) ( 1 + r3 ) ( 1 + r 2 ) ( 1 + r1 ) The discounting is incorrect in the model, and is carried through for periods two and greater. Appendix IV provides a more detailed discussion of the model calculations, including the monthly after-tax “discount rate” mentioned above. Page 29 GAO-03-513 Savings Bonds Appendix III Future Value Examples for Series EE and Series I Savings Bonds for Bonds 5 Years and Older Appen Ix di All calculations of interest are based on a hypothetical savings bond with a denomination of $25,1 such that for the following: Series EE, FV = PV * {[1+(i/2)](m/6)} Example: An EE savings bond rate of 5.07 percent will result in a newly purchased hypothetical $25 bond increasing in value after 6 months to $12.82, when rounded to the nearest cent. At the beginning of the first semiannual rate period, the present value (PV) is equal to $12.50 such that Month 1: FV = 12.50 * {[1 + (.0507/2)](1/6) = 12.55 Month 2: FV = 12.50 * {[1 + (.0507/2)](2/6) = 12.60 Month 3: FV = 12.50 * {[1 + (.0507/2)](3/6) = 12.66 Month 4: FV = 12.50 * {[1 + (.0507/2)](4/6) = 12.71 Month 5: FV = 12.50 * {[1 + (.0507/2)](5/6) = 12.76 Month 6: FV = 12.50 * {[1 + (.0507/2)](6/6) = 12.82 Thus, a $5,000 bond purchased at the same time as the hypothetical $25 bond will be worth $2,564 after 6 months ([$5,000 ÷ $25] x $12.82 = $2,564). The PV variable changes in months 7 through 12 such that the PV is equal to the redemption value at the beginning of the semiannual rate period, which in the above example is equal to month 6 future value (FV) such that Month 7: FV = 12.82 * {[1 + (.0507/2)](1/6) = 12.87 Month 8: FV = 12.82 * {[1 + (.0507/2)](2/6) = 12.93 Month 9: FV = 12.82 * {[1 + (.0507/2)](3/6) = 12.98 Month 10: FV = 12.82 * {[1 + (.0507/2)](4/6) = 13.04 Month 11: FV = 12.82 * {[1 + (.0507/2)](5/6) = 13.09 Month 12: FV = 12.82 * {[1 + (.0507/2)](6/6) = 13.14 The PV variable changes in months 13 through 18 such that the PV is equal to the redemption value at the beginning of the semiannual rate period, which in the above example is equal to month 12 FV, and so on. Sources: 31C.F.R. § 351.2-(k)(4)(ii)(A), U.S. Savings Bond Series EE Information Statement for bonds issued May 1997 or later, and GAO analysis. Note: Savings bonds are subject to a 12-month holding period and those redeemed before 5 years are subject to a 3-month interest penalty. 1 Series EE - 31C.F.R. §351.2-(k)(1)(iii); Series I – 31C.F.R. § 359.2-(e)(1)(vi). Page 30 GAO-03-513 Savings Bonds Appendix III Future Value Examples for Series EE and Series I Savings Bonds for Bonds 5 Years and Older Series I, FV = PV * {[1+(CR/2)](m/6)} Example: An I composite rate of 5.07 percent will result in a newly purchased hypothetical $25 bond increasing in value after 6 months to $25.63, when rounded to the nearest cent. At the beginning of the first semiannual rate period, the PV is equal to $25 such that Month 1: FV = 25 * {[1 + (.0507/2)](1/6) = 25.10 Month 2: FV = 25 * {[1 + (.0507/2)](2/6) = 25.21 Month 3: FV = 25 * {[1 + (.0507/2)](3/6) = 25.31 Month 4: FV = 25 * {[1 + (.0507/2)](4/6) = 25.42 Month 5: FV = 25 * {[1 + (.0507/2)](5/6) = 25.53 Month 6: FV = 25 * {[1 + (.0507/2)](6/6) = 25.63 Thus, a $5,000 bond purchased at the same time as the hypothetical $25 bond will be worth $5,126 after 6 months ([$5,000 ÷ $25] x $25.63 = $5,126). The PV variable changes in months 7 through 12 such that the PV is equal to the redemption value at the beginning of the semiannual rate period, which in the above example is equal to month 6 FV such that Month 7: FV = 25.63 * {[1 + (.0507/2)](1/6) = 25.74 Month 8: FV = 25.63 * {[1 + (.0507/2)](2/6) = 25.84 Month 9: FV = 25.63 * {[1 + (.0507/2)](3/6) = 25.95 Month 10: FV = 25.63 * {[1 + (.0507/2)](4/6) = 26.06 Month 11: FV = 25.63 * {[1 + (.0507/2)](5/6) = 26.17 Month 12: FV = 25.63 * {[1 + (.0507/2)](6/6) = 26.28 The PV variable changes in months 13 through 18 such that the PV is equal to the redemption value at the beginning of the semiannual rate period, which in the above example is equal to month 12 FV, and so on. Sources: 31C.F.R. § 359.2-(e)(4)(ii)(A), U.S. Savings Bond Series I Information Statement, and GAO analysis. Note: Savings bonds are subject to a 12-month holding period and those redeemed before 5 years are subject to a 3-month interest penalty. Page 31 GAO-03-513 Savings Bonds Appendix IV Model Calculations Detail Appen V Id xi The cost-effectiveness calculations in the Series EE and Series I submodels, as well as preceding steps, are similar; coding changes are due to the different structures of the two series, as noted in table 3, and modeling errors, as previously discussed. Though not shown here, both submodel calculations for savings bond redemption value incorporate the 3-month interest penalty for bonds redeemed before 5 years from issue. Calculations for Marketable Treasury “Present Value” — Five Steps Where n = months outstanding Step 1: Savings bond redemption valuen respective to denomination (as previously shown in table 3). Step 2: Savings bond redemption valuen after unit cost to redeem and tax revenue implications = Adjusted Redemption Valuen: Redemption Valuen – ((Redemption Valuen – savings bond issue price) * savings bond tax recovery rate) + unit cost to redeem1 Step 3: Algebraic after-tax “present value discount factor”n (comprising several component calculations): 3a. after-tax semiannual CMTn = (6-month average of CMTn/2) * (1 – tax recovery rate) 3b. after-tax semiannual CMTn expressed as a monthly rate = Yn = ((after-tax semiannual CMTn + 1) ^ (1/6)) – 1 3c. Yn algebraic conversion leading to after-tax “present value discount factor”: 3c.1. Sn = 1/(1 + Yn) 3.c.2 Month 1 FAC (that is, FAC1) = S1; for all other n, FACn = Sn * (FACn-1 + 1) 3d. After-tax “present value discount factor”n = FACTn = 1 – (Yn * FACn) Step 4: Algebraic after-tax “present value discount factor”n expressed as a monthly rate: Ien = (((1/FACTn) ^ (1/n)) – 1) 1 Adjusted for the education bond program such that savings bond tax recovery = tax recovery rate provided by the Treasury’s Office of Tax Policy * ( 1 - .10). Page 32 GAO-03-513 Savings Bonds Appendix IV Model Calculations Detail Step 5: Treasury “present value”n: Adjusted Redemption Valuen / (1 + Ien) ^ n The resulting marketable Treasury “present value”n = Adjusted Redemption Valuen * FACTn , which returns the following: Month 1 marketable Treasury “present value” = Adjusted Redemption Value1 - Adjusted Redemption Value1 * Y1 / (1 + Y1) Month 2 marketable Treasury “present value” = Adjusted Redemption Value2 – [Adjusted Redemption Value2 * Y2 / (1 + Y2) + Adjusted Redemption Value2 * Y2 / (1 + Y2)( 1 + Y1)], and so on. Calculation for Savings Bond “Present Value” — One Step Savings bond issue price respective to denomination – savings bond unit cost to issue Calculations for Cost-effectiveness Ratio — Six Steps Where n = months outstanding Step 1: “present value” differencen Savings bond “present value” - marketable Treasury “present value”n Step 2: Bonds redeemedn: Month 0 bonds redeemed = probability of redemption0 * savings bond sales volume respective to denomination Month 1 bonds redeemed = probability of redemption1 * (savings bond sales volume respective to denomination – bonds redeemed0); for all other bonds redeemedn = probability of redemptionn * (savings bond sales volume respective to denomination – bonds redeemed0..n) Step 3: Projected “present value” differencen: “present value” differencen * bonds redeemedn Step 4: Cumulative projected “present value” difference: Month 0 cumulative projected “present value” difference = projected “present value” difference0; for all other cumulative projected “present value” differencen = projected “present value” differencen + cumulative projected “present value” differencen-1 Page 33 GAO-03-513 Savings Bonds Appendix IV Model Calculations Detail Step 5: Bonds outstandingn: Month 0 bonds outstanding = sales volume respective to denomination – bonds redeemed0; for all other bonds outstandingn = bonds outstandingn-1 - bonds redeemedn Step 6: Cost-effectiveness ratio for each denomination (comprising several component calculations): 6a. (cumulative projected “present value” difference50 years – pieces outstanding50 years * savings bond unit cost to issue) 6b. (sales volume respective to denomination * savings bond issue price) 6c. (result of 6a. / results of 6b.) * 1,000 The resulting cost-effectiveness calculation returns a ratio of millions saved per $1 billion borrowed. Additional Calculations That Are Not Relevant to the Model’s Cost- effectiveness Calculation Though not detailed above, the model includes five calculations that do not produce output relevant to the cost-effectiveness calculation. In addition, the model performs an additional step in the after-tax “present value discount factor” calculation that is not necessary. The model creates an after-tax “present value discount factor” expressed as a monthly rate, shown above as step 4 in the calculations for the marketable Treasury “present value.” Step 5, as shown above in the calculations for the marketable Treasury “present value,” reverses this calculation through the 30-year life cycle of the marketable Treasury alternative. Page 34 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt Appen V di x Note: GAO comments supplementing those in the report text appear at the end of this appendix. Page 35 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt Page 36 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt Page 37 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt See comment 1. Page 38 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt Page 39 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt Page 40 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt See comment 2. See comment 3. Page 41 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt See comment 4. Page 42 GAO-03-513 Savings Bonds Appendix V Comments from the Bureau of the Public Debt GAO Comments The following are GAO's comments on the Bureau of the Public Debt's (BPD) letter dated June 4, 2003. 1. As we note in this report's Agency Comments and Our Evaluation section, the approach that BPD outlines here would be an appropriate alternative to the cost-effectiveness model based on a present value analysis described in the report. The description in this report is based on documentation for the cost-effectiveness model that BPD provided in an October 16, 2002, meeting; on a July 2002 report that BPD prepared for the House Committees on Appropriations and on Financial Services; and on March 2002 testimony by the Commissioner of the Public Debt before the House Appropriations Subcommittee on Treasury, Postal Service, and General Government. 2. As we note in the report, the 20-year extension is not consistent with a statement previously made by the Department of the Treasury regarding the presumption of payment 10 years beyond the maturity date. We agree that all administrative costs are included in the model. As the report notes, however, the model calculation does not accurately incorporate these costs in computing the present value of the marketable Treasury security and the savings bond. 3. Based on BPD's explanation that redemptions within 6 months of a savings bond's issuance are sometimes granted in hardship cases, we have deleted discussion of their inclusion in the model from the report. 4. As we note in the report, the model's compound interest formula for the Series I bonds does not recognize the bond's accrued value at the beginning of each semiannual period. When calculated out over 30 years, the difference between the formula in the regulation and the model's calculation is minor but still exists. Page 43 GAO-03-513 Savings Bonds Appendix VI GAO Contacts and Staff Acknowledgments AppenV d xiI GAO Contacts Thomas J. McCool, (202) 512-8678 James M. McDermott, (202) 512-5373 Acknowledgments In addition to those named above, Heather T. Dignan, Mitchell B. Rachlis, and Barbara M. Roesmann made key contributions to this report. (250098) Page 44 GAO-03-513 Savings Bonds GAO’s Mission The General Accounting Office, the audit, evaluation and investigative arm of Congress, exists to support Congress in meeting its constitutional responsibilities and to help improve the performance and accountability of the federal government for the American people. GAO examines the use of public funds; evaluates federal programs and policies; and provides analyses, recommendations, and other assistance to help Congress make informed oversight, policy, and funding decisions. GAO’s commitment to good government is reflected in its core values of accountability, integrity, and reliability. Obtaining Copies of The fastest and easiest way to obtain copies of GAO documents at no cost is through the Internet. GAO’s Web site (www.gao.gov) contains abstracts and full- GAO Reports and text files of current reports and testimony and an expanding archive of older products. 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## Savings Bonds: Actions Needed to Increase the Reliability of Cost-effectiveness Measures

#### Published by the Government Accountability Office on 2003-06-16.

Below is a raw (and likely hideous) rendition of the original report. (PDF)