Savings Bonds: Actions Needed to Increase the Reliability of Cost-effectiveness Measures
Published: 2003-06-16T00:00:00

Fast Facts:

Highlights:
section_title: Why GAO Did This Study
paragraphs: While the Treasury generally pays lower interest rates on U.S. Savings Bonds than it does on other forms of borrowing from the public, it also incurs substantially higher administrative costs to issue and redeem the paper savings bond certificates. To determine whether these higher administrative costs exceed its interest rate savings, Treasury's Bureau of the Public Debt uses a spreadsheet model to compare the costs of issuing Series EE and Series I savings bonds with those of issuing marketable Treasury securities. GAO was asked to review this model to judge its reliability in measuring the relative costs of Treasury's borrowing alternatives.
section_title: What GAO Found
paragraphs: Treasury has several alternative vehicles for issuing debt to the public. A substantial majority of that debt is issued in the form of marketable Treasury securities. U.S. Savings Bonds today account for about 3 percent of total Treasury securities outstanding. A majority of these bonds have lower minimum denominations or face amounts than marketable Treasury securities and generally pay lower interest rates as well, but provide the same assurance of the full faith and credit of the United States, making them an alternative for investors unable or unwilling to pay the minimum denominations of marketable Treasury securities. Savings bonds continue to be issued as paper certificates, rather than in the format of the "book entry" system for marketable Treasury securities; however, this increases the administrative costs of issuing, servicing, and redeeming savings bonds, relative to the marketable securities. The cost-effectiveness of the savings bond program depends on whether Treasury's savings--in terms of the generally lower interest payments on savings bonds relative to marketable Treasury securities--exceed the costs 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. As prescribed by the Office of Management and Budget and common financial practice, in dealing with savings or costs over time, the value of future savings or costs must be discounted to present value. Treasury has reported that its cost-effectiveness model does calculate the present values of the relative costs of savings bonds and marketable Treasury securities. However, because of flaws in the design and implementation of the spreadsheet used to calculate these present values, the cost-effectiveness model's results do not provide the Bureau of the Public Debt, Treasury, or 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.

section_title: Letter
paragraphs: 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.  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.
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.
subsections: section_title: Background
paragraphs: 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.
subsections: section_title: Savings Bond Program
paragraphs: 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.
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.
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.
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. 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.
section_title: Savings Bond Cost- effectiveness Model
paragraphs: 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. 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. 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).
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.
section_title: Conceptual Design for Estimating Savings Bond Cost- effectiveness Is Appropriate, but Model Calculations Contain Errors
paragraphs: OMB guidelines state that a cost-effectiveness analysis is appropriate to  use in an analysis of government programs when the benefits of competing  alternatives are the same or where a policy decision has been made that the  benefits of a program must be provided. A program is cost effective if, on  the basis of life cycle cost analysis of competing alternatives, it is  determined to have the lowest costs expressed in present value terms for a  given amount of benefits. The conceptual design underlying the savings  bond cost-effectiveness model reflects this OMB guidance. However, the  present value calculations in the model contain errors. As a result, the  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.
subsections: section_title: Model’s Conceptual Design Follows OMB Guidelines
paragraphs: The model’s conceptual design follows OMB guidelines for cost- effectiveness analysis. Figure 1 shows the conceptual design of the 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  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). 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), and (2) reducing the  present value of the marketable Treasury security by subtracting its  estimated (that is, not paid) “discounted” coupons.
section_title: Model Creates Cost- effectiveness Ratio Based on Calculated “Present Values” for Both Alternatives
paragraphs: In general, the model is conceptually designed to create a marketable  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  that of a savings bond’s net cost to Treasury (that is, redemption value  adjusted for administrative unit costs and tax revenue implications). The  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. 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.
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. 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.
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. 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.
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.
section_title: BPD’s Definition of Present Value Does Not Follow OMB Guidance
paragraphs: Although Treasury has presented the model as measuring cost- 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  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  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.
section_title: Key Model Parameters and Components May Not Be Reliable
paragraphs: 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.  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.  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.
subsections: section_title: Despite Enhancements, Model Results May Not Be Accurate
paragraphs: The first enhancement affects a key calculation in the savings bond cost- effectiveness model: the redemption value, or future value, of the savings  bond over time. These values form the basis for constructing a marketable  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  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.
section_title: Discontinuance of 30-Year Marketable Treasury Bonds Directly Affects the Marketable Yield Model Parameter
paragraphs: A BPD official told us that the equivalent marketable yield, or CMT, has the  strongest impact on model results. The CMT is the basis for BPD’s  “discount factor” used to derive the “present value” of the alternative  marketable Treasury security. Treasury discontinued the issuance of the 30- year Treasury bond in October 2001, however, directly affecting how the  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. BPD staff told us that BPD is still considering how to reflect this  change in the model’s “discount factor.”
section_title: Other Model Features Could Affect the Reliability of Model Results
paragraphs: The model coding contains additional inaccuracies that, in comparison to  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  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.
In addition, the savings bond cost-effectiveness model is maintained in  older software. 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.
section_title: BPD Has Not Requested an Independent External Review of the Model
paragraphs: While OMB guidance calls for an independent external review of cost- effectiveness models, as well as assessments of their accuracy and  reliability, BPD has not commissioned such analysis. As a result, BPD  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  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.
section_title: Conclusions
paragraphs: 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  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.
section_title: Recommendations
paragraphs: 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  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.
section_title: Agency Comments and Our Evaluation
paragraphs: 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  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.
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.”
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  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  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.
section_title: Objectives, Scope, and Methodology
paragraphs: 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.
section_title: Present Value Theory and Model Calculations
paragraphs: 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. ... ... ... ... ... ----------------------------1 +( )
In many explanations of present value, the discount rate is held constant, removing the  need for r-1, to vary over time.
0=  (coupon + face) =  ----------------------------------------------- ---------------------------------------------- , in which ) ) ) )*...* 1 ) for some t >2, for example.
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). ----------------1 r+( )
In the illustrations above, the rate or rates used to discount each  component is relevant to the time period.
Model Calculation for the “Present Value” of the Marketable Treasury  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 Value1*r1 ------------------------------------------------------- )
Redemption Value2* r2 -------------------------------------------------------- )
Redemption Value2* r2 -------------------------------------------------------- )
subsections: section_title: Redemption Value3
paragraphs: Redemption Value3* r3 -------------------------------------------------------- )
Redemption Value3* r3 -------------------------------------------------------- )
Redemption Value3* r3 --------------------------------------------------------r2+(r1+() 1) 1 r3+(1 )
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.
section_title: Future Value Examples for Series EE and Series I Savings Bonds for Bonds 5 Years and Older
paragraphs: Series EE - 31C.F.R. §351.2-(k)(1)(iii); Series I – 31C.F.R. § 359.2-(e)(1)(vi).
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 * {(1/6) = 25.10  Month 2: FV = 25 * {(2/6) = 25.21  Month 3: FV = 25 * {(3/6) = 25.31  Month 4: FV = 25 * {(4/6) = 25.42  Month 5: FV = 25 * {(5/6) = 25.53  Month 6: FV = 25 * {(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  ( 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 * {(1/6) = 25.74  Month 8:   FV = 25.63 * {(2/6) = 25.84  Month 9:   FV = 25.63 * {(3/6) = 25.95  Month 10: FV = 25.63 * {(4/6) = 26.06  Month 11: FV = 25.63 * {(5/6) = 26.17  Month 12: FV = 25.63 * {(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.
section_title: Model Calculations Detail
paragraphs: 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 value respective to denomination (as  previously shown in table 3).
Step 2: Savings bond redemption value after unit cost to redeem and tax  revenue implications = Adjusted Redemption Value:  Redemption Value – ((Redemption Value – savings bond issue  price) * savings bond tax recovery rate) + unit cost to redeemStep 3: Algebraic after-tax “present value discount factor”several component calculations): 3a. after-tax semiannual CMT= (6-month average of CMT/2) *  (1 – tax recovery rate) 3b. after-tax semiannual CMT expressed as a monthly rate = Y =  ((after-tax semiannual CMT + 1) ^ (1/6)) – 1 3c. Y algebraic conversion leading to after-tax “present value  3c.1. S = 1/(1 + Y) 3.c.2 Month 1 FAC (that is, FAC; for all other n, FAC = S  * (FACn-1 + 1)  3d. After-tax “present value discount factor” = 1 – (Y *  FAC)
Step 4: Algebraic after-tax “present value discount factor”monthly rate: Ie = (((1/FACT) ^ (1/n)) – 1)
Step 5: Treasury “present value” / (1 + Ie) ^ The resulting marketable Treasury “present value” * FACT , which returns the following: Month 1 marketable Treasury “present value” = Adjusted Redemption  Value - Adjusted Redemption Value / (1 + Y * Y) + Adjusted Redemption  Value / (1 + Y)], and so on.
Savings bond “present value” - marketable Treasury “present  value”
Month 0 bonds redeemed = probability of redemption *  (savings bond sales volume respective to denomination – bonds  redeemed0..n)
Month 0 bonds outstanding = sales volume respective to  denomination – bonds redeemed  = bonds outstandingn-1 -  bonds redeemedStep 6: Cost-effectiveness ratio for each denomination (comprising several  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.
section_title: Comments from the Bureau of the Public Debt
subsections: section_title: GAO Comments
paragraphs: 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.
section_title: GAO Contacts and Staff Acknowledgments
subsections: section_title: GAO Contacts
section_title: Acknowledgments
paragraphs: In addition to those named above, Heather T. Dignan, Mitchell B. Rachlis,  and Barbara M. Roesmann made key contributions to this report.
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